Derivative function：
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Enter an original function (that is, the function to be derived), then set the variable to be derived and the order of the derivative, and click the "Next" button to obtain the derivative function of the corresponding order of the function.
Note that the input function supports mathematical functions and other constants.
Current location：Derivative function > Derivative function calculation history > Answer
There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{((x - 1){(x - 3)}^{2}{(x - 4)}^{3}abs(x - 6))}{((x - 2){(x - 5)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{25absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{261absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{1471absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{4810absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{9048absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{8928absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{3456abs}{(x^{3} - 12x^{2} + 45x - 50)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{25absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{261absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{1471absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{4810absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{9048absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{8928absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{3456abs}{(x^{3} - 12x^{2} + 45x - 50)}\right)}{dx}\\=&(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{7} + \frac{abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)} - 25(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{6} - \frac{25abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)} + 261(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{5} + \frac{261abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)} - 1471(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{4} - \frac{1471abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + 4810(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{3} + \frac{4810abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)} - 9048(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{2} - \frac{9048abs*2x}{(x^{3} - 12x^{2} + 45x - 50)} + 8928(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx + \frac{8928abs}{(x^{3} - 12x^{2} + 45x - 50)} - 3456(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})abs + 0\\=&\frac{-3absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{99absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{7absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{1428absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{11802absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{150absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{61479absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{1305absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{208779absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{460386absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{5884absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{631800absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{14430absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{18096absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{484704absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{8928abs}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{155520abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{99absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{7absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{1428absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{11802absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{150absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{61479absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{1305absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{208779absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{460386absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{5884absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{631800absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{14430absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{18096absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{484704absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{8928abs}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{155520abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}}\right)}{dx}\\=&-3(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{9} - \frac{3abs*9x^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 99(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{8} + \frac{99abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 7(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{6} + \frac{7abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - 1428(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{7} - \frac{1428abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 11802(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{6} + \frac{11802abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 150(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{5} - \frac{150abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)} - 61479(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{5} - \frac{61479abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 1305(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{4} + \frac{1305abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + 208779(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{4} + \frac{208779abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 460386(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{3} - \frac{460386abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 5884(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{3} - \frac{5884abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + 631800(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{2} + \frac{631800abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 14430(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{2} + \frac{14430abs*2x}{(x^{3} - 12x^{2} + 45x - 50)} - 18096(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx - \frac{18096abs}{(x^{3} - 12x^{2} + 45x - 50)} - 484704(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx - \frac{484704abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 8928(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})abs + 0 + 155520(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})abs + 0\\=&\frac{18absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{738absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{48absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{13590absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{148266absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1410absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{42absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{1063890absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{17826absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{5265846absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{18316818absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{126534absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{750absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{44679438absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{550626absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{5220absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{74669364absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{81060912absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1500504absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{2491596absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{17652absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{2292192absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{28860absx}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{51088320absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{18096abs}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{886464abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{13996800abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{18absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{738absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{48absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{13590absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{148266absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1410absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{42absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{1063890absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{17826absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{5265846absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{18316818absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{126534absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{750absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{44679438absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{550626absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{5220absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{74669364absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{81060912absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1500504absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{2491596absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{17652absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{2292192absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{28860absx}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{51088320absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{18096abs}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{886464abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{13996800abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}}\right)}{dx}\\=&18(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{11} + \frac{18abs*11x^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 738(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{10} - \frac{738abs*10x^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 48(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{8} - \frac{48abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 13590(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{9} + \frac{13590abs*9x^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 148266(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{8} - \frac{148266abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 1410(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{7} + \frac{1410abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 42(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{5} + \frac{42abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + 1063890(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{7} + \frac{1063890abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 17826(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{6} - \frac{17826abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 5265846(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{6} - \frac{5265846abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 18316818(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{5} + \frac{18316818abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 126534(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{5} + \frac{126534abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 750(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{4} - \frac{750abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)} - 44679438(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{4} - \frac{44679438abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 550626(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{4} - \frac{550626abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 5220(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{3} + \frac{5220abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + 74669364(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{3} + \frac{74669364abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 81060912(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{2} - \frac{81060912abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 1500504(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{3} + \frac{1500504abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 2491596(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{2} - \frac{2491596abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 17652(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{2} - \frac{17652abs*2x}{(x^{3} - 12x^{2} + 45x - 50)} + 2292192(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx + \frac{2292192abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 28860(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx + \frac{28860abs}{(x^{3} - 12x^{2} + 45x - 50)} + 51088320(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx + \frac{51088320abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 18096(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})abs + 0 - 886464(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})abs + 0 - 13996800(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})abs + 0\\=&\frac{-162absx^{13}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{7938absx^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{486absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{177876absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{2412504absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{18144absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{510absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{22084812absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{301266absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{144008604absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{687617424absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{2927880absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{13128absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{210absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{2431815048absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{18428958absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{142506absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{6361714242absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{12137466546absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{78416208absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{16376544684absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{228114198absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{844656absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{3000absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{14747553360absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{447112872absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{2947632absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{15660absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{563595732absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{410969376absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{6042780absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{6716196absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{35304absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{7904692800absx}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{28860abs}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{3106512abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{130870080abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1889568000abs}{(x^{3} - 12x^{2} + 45x - 50)^{4}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-162absx^{13}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{7938absx^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{486absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{177876absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{2412504absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{18144absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{510absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{22084812absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{301266absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{144008604absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{687617424absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{2927880absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{13128absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{210absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{2431815048absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{18428958absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{142506absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{6361714242absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{12137466546absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{78416208absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{16376544684absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{228114198absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{844656absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{3000absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{14747553360absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{447112872absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{2947632absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{15660absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{563595732absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{410969376absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{6042780absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{6716196absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{35304absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{7904692800absx}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{28860abs}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{3106512abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{130870080abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1889568000abs}{(x^{3} - 12x^{2} + 45x - 50)^{4}}\right)}{dx}\\=&-162(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{13} - \frac{162abs*13x^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 7938(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{12} + \frac{7938abs*12x^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 486(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{10} + \frac{486abs*10x^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 177876(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{11} - \frac{177876abs*11x^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 2412504(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{10} + \frac{2412504abs*10x^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 18144(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{9} - \frac{18144abs*9x^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 510(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{7} - \frac{510abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 22084812(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{9} - \frac{22084812abs*9x^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 301266(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{8} + \frac{301266abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 144008604(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{8} + \frac{144008604abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 687617424(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{7} - \frac{687617424abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 2927880(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{7} - \frac{2927880abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 13128(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{6} + \frac{13128abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 210(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{4} + \frac{210abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + 2431815048(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{6} + \frac{2431815048abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 18428958(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{6} + \frac{18428958abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 142506(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{5} - \frac{142506abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 6361714242(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{5} - \frac{6361714242abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 12137466546(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{4} + \frac{12137466546abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 78416208(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{5} - \frac{78416208abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 16376544684(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{3} - \frac{16376544684abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 228114198(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{4} + \frac{228114198abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 844656(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{4} + \frac{844656abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 3000(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{3} - \frac{3000abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + 14747553360(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{2} + \frac{14747553360abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 447112872(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{3} - \frac{447112872abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 2947632(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{3} - \frac{2947632abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 15660(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{2} + \frac{15660abs*2x}{(x^{3} - 12x^{2} + 45x - 50)} + 563595732(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{2} + \frac{563595732abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 410969376(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx - \frac{410969376abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 6042780(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{2} + \frac{6042780abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 6716196(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx - \frac{6716196abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 35304(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx - \frac{35304abs}{(x^{3} - 12x^{2} + 45x - 50)} - 7904692800(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx - \frac{7904692800abs}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 28860(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})abs + 0 + 3106512(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})abs + 0 + 130870080(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})abs + 0 + 1889568000(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})abs + 0\\=&\frac{1944absx^{15}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{110808absx^{14}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{6480absx^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{2925720absx^{13}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{47454984absx^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{293544absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{7920absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{528635808absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{6040008absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{4282495920absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{26051501232absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{74616552absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{266544absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{4200absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{121114602000absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{616102200absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{3941208absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{433565951832absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{1194100874424absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{3579963480absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{2506823888184absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{15000226056absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{33584904absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{92808absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{840absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{3933862908264absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{4458399479280absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{45625316472absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{181628568absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{840960absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{3436084929600absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{99868476312absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{153187720992absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{645843096absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{155982683664absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{1508094288absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{3995376absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{9000absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{94398618240absx}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{2226205296absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{10481472absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{31320absx}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{1880761680absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{14366880absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{1604243232000absx}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{8014896abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{35304abs}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{690555456abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{25572153600abs}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{340122240000abs}{(x^{3} - 12x^{2} + 45x - 50)^{5}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{((x - 1){(x - 3)}^{2}{(x - 4)}^{3}abs(x - 6))}{((x - 2){(x - 5)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{25absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{261absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{1471absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{4810absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{9048absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{8928absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{3456abs}{(x^{3} - 12x^{2} + 45x - 50)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{25absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{261absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{1471absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{4810absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{9048absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{8928absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{3456abs}{(x^{3} - 12x^{2} + 45x - 50)}\right)}{dx}\\=&(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{7} + \frac{abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)} - 25(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{6} - \frac{25abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)} + 261(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{5} + \frac{261abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)} - 1471(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{4} - \frac{1471abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + 4810(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{3} + \frac{4810abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)} - 9048(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{2} - \frac{9048abs*2x}{(x^{3} - 12x^{2} + 45x - 50)} + 8928(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx + \frac{8928abs}{(x^{3} - 12x^{2} + 45x - 50)} - 3456(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})abs + 0\\=&\frac{-3absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{99absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{7absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{1428absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{11802absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{150absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{61479absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{1305absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{208779absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{460386absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{5884absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{631800absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{14430absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{18096absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{484704absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{8928abs}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{155520abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-3absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{99absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{7absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{1428absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{11802absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{150absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{61479absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{1305absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{208779absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{460386absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{5884absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{631800absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{14430absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{18096absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{484704absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{8928abs}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{155520abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}}\right)}{dx}\\=&-3(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{9} - \frac{3abs*9x^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 99(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{8} + \frac{99abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 7(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{6} + \frac{7abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)} - 1428(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{7} - \frac{1428abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 11802(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{6} + \frac{11802abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 150(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{5} - \frac{150abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)} - 61479(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{5} - \frac{61479abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 1305(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{4} + \frac{1305abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + 208779(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{4} + \frac{208779abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 460386(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{3} - \frac{460386abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 5884(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{3} - \frac{5884abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + 631800(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{2} + \frac{631800abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 14430(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{2} + \frac{14430abs*2x}{(x^{3} - 12x^{2} + 45x - 50)} - 18096(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx - \frac{18096abs}{(x^{3} - 12x^{2} + 45x - 50)} - 484704(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx - \frac{484704abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 8928(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})abs + 0 + 155520(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})abs + 0\\=&\frac{18absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{738absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{48absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{13590absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{148266absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1410absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{42absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{1063890absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{17826absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{5265846absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{18316818absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{126534absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{750absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{44679438absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{550626absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{5220absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{74669364absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{81060912absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1500504absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{2491596absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{17652absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{2292192absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{28860absx}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{51088320absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{18096abs}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{886464abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{13996800abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{18absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{738absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{48absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{13590absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{148266absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1410absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{42absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{1063890absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{17826absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{5265846absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{18316818absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{126534absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{750absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{44679438absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{550626absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{5220absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{74669364absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{81060912absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1500504absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{2491596absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{17652absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{2292192absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{28860absx}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{51088320absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{18096abs}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{886464abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{13996800abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}}\right)}{dx}\\=&18(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{11} + \frac{18abs*11x^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 738(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{10} - \frac{738abs*10x^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 48(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{8} - \frac{48abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 13590(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{9} + \frac{13590abs*9x^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 148266(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{8} - \frac{148266abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 1410(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{7} + \frac{1410abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 42(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{5} + \frac{42abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + 1063890(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{7} + \frac{1063890abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 17826(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{6} - \frac{17826abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 5265846(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{6} - \frac{5265846abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 18316818(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{5} + \frac{18316818abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 126534(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{5} + \frac{126534abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 750(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{4} - \frac{750abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)} - 44679438(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{4} - \frac{44679438abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 550626(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{4} - \frac{550626abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 5220(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{3} + \frac{5220abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + 74669364(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{3} + \frac{74669364abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 81060912(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{2} - \frac{81060912abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 1500504(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{3} + \frac{1500504abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 2491596(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{2} - \frac{2491596abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 17652(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{2} - \frac{17652abs*2x}{(x^{3} - 12x^{2} + 45x - 50)} + 2292192(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx + \frac{2292192abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 28860(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx + \frac{28860abs}{(x^{3} - 12x^{2} + 45x - 50)} + 51088320(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx + \frac{51088320abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 18096(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})abs + 0 - 886464(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})abs + 0 - 13996800(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})abs + 0\\=&\frac{-162absx^{13}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{7938absx^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{486absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{177876absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{2412504absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{18144absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{510absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{22084812absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{301266absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{144008604absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{687617424absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{2927880absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{13128absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{210absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{2431815048absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{18428958absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{142506absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{6361714242absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{12137466546absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{78416208absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{16376544684absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{228114198absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{844656absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{3000absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{14747553360absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{447112872absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{2947632absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{15660absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{563595732absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{410969376absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{6042780absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{6716196absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{35304absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{7904692800absx}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{28860abs}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{3106512abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{130870080abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1889568000abs}{(x^{3} - 12x^{2} + 45x - 50)^{4}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-162absx^{13}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{7938absx^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{486absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{177876absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{2412504absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{18144absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{510absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{22084812absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{301266absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{144008604absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{687617424absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{2927880absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{13128absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{210absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{2431815048absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{18428958absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{142506absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{6361714242absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{12137466546absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{78416208absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{16376544684absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{228114198absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{844656absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{3000absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{14747553360absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{447112872absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{2947632absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{15660absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{563595732absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{410969376absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{6042780absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{6716196absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{35304absx}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{7904692800absx}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{28860abs}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{3106512abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{130870080abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{1889568000abs}{(x^{3} - 12x^{2} + 45x - 50)^{4}}\right)}{dx}\\=&-162(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{13} - \frac{162abs*13x^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 7938(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{12} + \frac{7938abs*12x^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 486(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{10} + \frac{486abs*10x^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 177876(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{11} - \frac{177876abs*11x^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 2412504(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{10} + \frac{2412504abs*10x^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 18144(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{9} - \frac{18144abs*9x^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 510(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{7} - \frac{510abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 22084812(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{9} - \frac{22084812abs*9x^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 301266(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{8} + \frac{301266abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 144008604(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{8} + \frac{144008604abs*8x^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 687617424(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{7} - \frac{687617424abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 2927880(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{7} - \frac{2927880abs*7x^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 13128(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{6} + \frac{13128abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 210(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{4} + \frac{210abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)} + 2431815048(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{6} + \frac{2431815048abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 18428958(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{6} + \frac{18428958abs*6x^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 142506(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{5} - \frac{142506abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 6361714242(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{5} - \frac{6361714242abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 12137466546(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{4} + \frac{12137466546abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 78416208(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{5} - \frac{78416208abs*5x^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 16376544684(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{3} - \frac{16376544684abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 228114198(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{4} + \frac{228114198abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 844656(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{4} + \frac{844656abs*4x^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 3000(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{3} - \frac{3000abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + 14747553360(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx^{2} + \frac{14747553360abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - 447112872(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{3} - \frac{447112872abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 2947632(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{3} - \frac{2947632abs*3x^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + 15660(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx^{2} + \frac{15660abs*2x}{(x^{3} - 12x^{2} + 45x - 50)} + 563595732(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx^{2} + \frac{563595732abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - 410969376(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})absx - \frac{410969376abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + 6042780(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx^{2} + \frac{6042780abs*2x}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 6716196(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})absx - \frac{6716196abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - 35304(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})absx - \frac{35304abs}{(x^{3} - 12x^{2} + 45x - 50)} - 7904692800(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})absx - \frac{7904692800abs}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + 28860(\frac{-(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{2}})abs + 0 + 3106512(\frac{-2(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{3}})abs + 0 + 130870080(\frac{-3(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{4}})abs + 0 + 1889568000(\frac{-4(3x^{2} - 12*2x + 45 + 0)}{(x^{3} - 12x^{2} + 45x - 50)^{5}})abs + 0\\=&\frac{1944absx^{15}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{110808absx^{14}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{6480absx^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{2925720absx^{13}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{47454984absx^{12}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{293544absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{7920absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{528635808absx^{11}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{6040008absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{4282495920absx^{10}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{26051501232absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{74616552absx^{9}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{266544absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{4200absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{121114602000absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{616102200absx^{8}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{3941208absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{433565951832absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{1194100874424absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{3579963480absx^{7}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{2506823888184absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{15000226056absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{33584904absx^{6}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{92808absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{840absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{3933862908264absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{4458399479280absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} + \frac{45625316472absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{181628568absx^{5}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{840960absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{3436084929600absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{99868476312absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{153187720992absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{645843096absx^{4}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{155982683664absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{4}} + \frac{1508094288absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{3995376absx^{3}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{9000absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{94398618240absx}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{2226205296absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{10481472absx^{2}}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{31320absx}{(x^{3} - 12x^{2} + 45x - 50)} + \frac{1880761680absx}{(x^{3} - 12x^{2} + 45x - 50)^{3}} + \frac{14366880absx}{(x^{3} - 12x^{2} + 45x - 50)^{2}} + \frac{1604243232000absx}{(x^{3} - 12x^{2} + 45x - 50)^{5}} - \frac{8014896abs}{(x^{3} - 12x^{2} + 45x - 50)^{2}} - \frac{35304abs}{(x^{3} - 12x^{2} + 45x - 50)} - \frac{690555456abs}{(x^{3} - 12x^{2} + 45x - 50)^{3}} - \frac{25572153600abs}{(x^{3} - 12x^{2} + 45x - 50)^{4}} - \frac{340122240000abs}{(x^{3} - 12x^{2} + 45x - 50)^{5}}\\ \end{split}\end{equation} \]