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 1 derivative of x is calculated.
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({x}^{5} + 4{x}^{4} + 10{x}^{3} + x + \frac{100}{x} + 1000{\frac{1}{x}}^{3} - \frac{sqrt({x}^{10} + {x}^{8})}{ln(x)})sin(\frac{sqrt({x}^{6})cos(x)}{100})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{5}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 4x^{4}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 10x^{3}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + xsin(\frac{1}{100}cos(x)sqrt(x^{6})) + \frac{100sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x} + \frac{1000sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{3}} - \frac{sin(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{10} + x^{8})}{ln(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{5}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 4x^{4}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 10x^{3}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + xsin(\frac{1}{100}cos(x)sqrt(x^{6})) + \frac{100sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x} + \frac{1000sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{3}} - \frac{sin(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{10} + x^{8})}{ln(x)}\right)}{dx}\\=&5x^{4}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + x^{5}cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}}) + 4*4x^{3}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 4x^{4}cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}}) + 10*3x^{2}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 10x^{3}cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}}) + sin(\frac{1}{100}cos(x)sqrt(x^{6})) + xcos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}}) + \frac{100*-sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{2}} + \frac{100cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}})}{x} + \frac{1000*-3sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{4}} + \frac{1000cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}})}{x^{3}} - \frac{-sin(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{10} + x^{8})}{ln^{2}(x)(x)} - \frac{cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}})sqrt(x^{10} + x^{8})}{ln(x)} - \frac{sin(\frac{1}{100}cos(x)sqrt(x^{6}))(10x^{9} + 8x^{7})*\frac{1}{2}}{ln(x)(x^{10} + x^{8})^{\frac{1}{2}}}\\=&\frac{-x^{5}sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{100} - \frac{x^{4}sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{25} + \frac{3x^{7}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{100} - \frac{x^{3}sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{10} - \frac{xsin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{100} + \frac{3x^{6}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{25} - \frac{sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{x} - \frac{10sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{x^{3}} + \frac{3x^{5}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{10} + sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 5x^{4}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + \frac{3x^{3}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{100} - \frac{100sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{2}} + 30x^{2}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 3xcos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x) - \frac{3000sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{4}} + 16x^{3}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + \frac{30cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{x} + \frac{sin(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{10} + x^{8})}{xln^{2}(x)} + \frac{sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})sqrt(x^{10} + x^{8})}{100ln(x)} - \frac{3x^{2}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)sqrt(x^{10} + x^{8})}{100ln(x)} - \frac{5x^{9}sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{(x^{10} + x^{8})^{\frac{1}{2}}ln(x)} - \frac{4x^{7}sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{(x^{10} + x^{8})^{\frac{1}{2}}ln(x)}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({x}^{5} + 4{x}^{4} + 10{x}^{3} + x + \frac{100}{x} + 1000{\frac{1}{x}}^{3} - \frac{sqrt({x}^{10} + {x}^{8})}{ln(x)})sin(\frac{sqrt({x}^{6})cos(x)}{100})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{5}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 4x^{4}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 10x^{3}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + xsin(\frac{1}{100}cos(x)sqrt(x^{6})) + \frac{100sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x} + \frac{1000sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{3}} - \frac{sin(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{10} + x^{8})}{ln(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{5}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 4x^{4}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 10x^{3}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + xsin(\frac{1}{100}cos(x)sqrt(x^{6})) + \frac{100sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x} + \frac{1000sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{3}} - \frac{sin(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{10} + x^{8})}{ln(x)}\right)}{dx}\\=&5x^{4}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + x^{5}cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}}) + 4*4x^{3}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 4x^{4}cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}}) + 10*3x^{2}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 10x^{3}cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}}) + sin(\frac{1}{100}cos(x)sqrt(x^{6})) + xcos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}}) + \frac{100*-sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{2}} + \frac{100cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}})}{x} + \frac{1000*-3sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{4}} + \frac{1000cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}})}{x^{3}} - \frac{-sin(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{10} + x^{8})}{ln^{2}(x)(x)} - \frac{cos(\frac{1}{100}cos(x)sqrt(x^{6}))(\frac{1}{100}*-sin(x)sqrt(x^{6}) + \frac{\frac{1}{100}cos(x)*6x^{5}*\frac{1}{2}}{(x^{6})^{\frac{1}{2}}})sqrt(x^{10} + x^{8})}{ln(x)} - \frac{sin(\frac{1}{100}cos(x)sqrt(x^{6}))(10x^{9} + 8x^{7})*\frac{1}{2}}{ln(x)(x^{10} + x^{8})^{\frac{1}{2}}}\\=&\frac{-x^{5}sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{100} - \frac{x^{4}sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{25} + \frac{3x^{7}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{100} - \frac{x^{3}sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{10} - \frac{xsin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{100} + \frac{3x^{6}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{25} - \frac{sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{x} - \frac{10sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})}{x^{3}} + \frac{3x^{5}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{10} + sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 5x^{4}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + \frac{3x^{3}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{100} - \frac{100sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{2}} + 30x^{2}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + 3xcos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x) - \frac{3000sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{x^{4}} + 16x^{3}sin(\frac{1}{100}cos(x)sqrt(x^{6})) + \frac{30cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)}{x} + \frac{sin(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{10} + x^{8})}{xln^{2}(x)} + \frac{sin(x)cos(\frac{1}{100}cos(x)sqrt(x^{6}))sqrt(x^{6})sqrt(x^{10} + x^{8})}{100ln(x)} - \frac{3x^{2}cos(\frac{1}{100}cos(x)sqrt(x^{6}))cos(x)sqrt(x^{10} + x^{8})}{100ln(x)} - \frac{5x^{9}sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{(x^{10} + x^{8})^{\frac{1}{2}}ln(x)} - \frac{4x^{7}sin(\frac{1}{100}cos(x)sqrt(x^{6}))}{(x^{10} + x^{8})^{\frac{1}{2}}ln(x)}\\ \end{split}\end{equation} \]