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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {2}^{(\frac{ln(x)}{(x - 1)})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {2}^{(\frac{ln(x)}{(x - 1)})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {2}^{(\frac{ln(x)}{(x - 1)})}\right)}{dx}\\=&({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))\\=&\frac{-{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x)}{(x - 1)^{2}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{-{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x)}{(x - 1)^{2}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x}\right)}{dx}\\=&-(\frac{-2(1 + 0)}{(x - 1)^{3}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x) - \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(2)ln(x)}{(x - 1)^{2}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*0ln(x)}{(x - 1)^{2}(2)} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{2}(x)} + \frac{(\frac{-(1 + 0)}{(x - 1)^{2}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{x} + \frac{-{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x^{2}} + \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(2)}{(x - 1)x} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*0}{(x - 1)x(2)}\\=&\frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x)}{(x - 1)^{3}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln^{2}(x)}{(x - 1)^{4}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{3}x} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{3}x} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x^{2}} - \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{2}x} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{2}x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x)}{(x - 1)^{3}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln^{2}(x)}{(x - 1)^{4}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{3}x} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{3}x} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x^{2}} - \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{2}x} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{2}x^{2}}\right)}{dx}\\=&2(\frac{-3(1 + 0)}{(x - 1)^{4}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x) + \frac{2({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(2)ln(x)}{(x - 1)^{3}} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}*0ln(x)}{(x - 1)^{3}(2)} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{3}(x)} + (\frac{-4(1 + 0)}{(x - 1)^{5}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln^{2}(x) + \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{2}(2)ln^{2}(x)}{(x - 1)^{4}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*2ln(2)*0ln^{2}(x)}{(x - 1)^{4}(2)} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)*2ln(x)}{(x - 1)^{4}(x)} - \frac{(\frac{-3(1 + 0)}{(x - 1)^{4}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{x} - \frac{-{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{3}x^{2}} - \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{2}(2)ln(x)}{(x - 1)^{3}x} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*2ln(2)*0ln(x)}{(x - 1)^{3}x(2)} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{3}x(x)} - \frac{(\frac{-3(1 + 0)}{(x - 1)^{4}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{x} - \frac{-{2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{3}x^{2}} - \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(x)ln^{2}(2)}{(x - 1)^{3}x} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{3}x(x)} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(x)*2ln(2)*0}{(x - 1)^{3}x(2)} - \frac{(\frac{-(1 + 0)}{(x - 1)^{2}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{x^{2}} - \frac{-2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x^{3}} - \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(2)}{(x - 1)x^{2}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*0}{(x - 1)x^{2}(2)} - \frac{2(\frac{-2(1 + 0)}{(x - 1)^{3}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{x} - \frac{2*-{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{2}x^{2}} - \frac{2({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(2)}{(x - 1)^{2}x} - \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}*0}{(x - 1)^{2}x(2)} + \frac{(\frac{-2(1 + 0)}{(x - 1)^{3}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{x^{2}} + \frac{-2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{2}x^{3}} + \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{2}(2)}{(x - 1)^{2}x^{2}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*2ln(2)*0}{(x - 1)^{2}x^{2}(2)}\\=&\frac{-6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x)}{(x - 1)^{4}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln^{2}(x)}{(x - 1)^{5}} + \frac{5 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{4}x} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{3}x^{2}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{3}(x)}{(x - 1)^{6}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{2}(x)}{(x - 1)^{5}x} + \frac{7 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{4}x} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{3}x^{2}} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(x)ln^{3}(2)}{(x - 1)^{5}x} - \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln(x)}{(x - 1)^{4}x^{2}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{3}(2)}{(x - 1)^{4}x^{2}} + \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{3}x} + \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{2}x^{2}} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x^{3}} - \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{2}x^{3}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{3}x^{2}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)}{(x - 1)^{3}x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{-6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x)}{(x - 1)^{4}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln^{2}(x)}{(x - 1)^{5}} + \frac{5 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{4}x} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{3}x^{2}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{3}(x)}{(x - 1)^{6}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{2}(x)}{(x - 1)^{5}x} + \frac{7 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{4}x} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{3}x^{2}} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(x)ln^{3}(2)}{(x - 1)^{5}x} - \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln(x)}{(x - 1)^{4}x^{2}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{3}(2)}{(x - 1)^{4}x^{2}} + \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{3}x} + \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{2}x^{2}} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x^{3}} - \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{2}x^{3}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{3}x^{2}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)}{(x - 1)^{3}x^{3}}\right)}{dx}\\=&-6(\frac{-4(1 + 0)}{(x - 1)^{5}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x) - \frac{6({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(2)ln(x)}{(x - 1)^{4}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}*0ln(x)}{(x - 1)^{4}(2)} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{4}(x)} - 6(\frac{-5(1 + 0)}{(x - 1)^{6}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln^{2}(x) - \frac{6({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{2}(2)ln^{2}(x)}{(x - 1)^{5}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}*2ln(2)*0ln^{2}(x)}{(x - 1)^{5}(2)} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)*2ln(x)}{(x - 1)^{5}(x)} + \frac{5(\frac{-4(1 + 0)}{(x - 1)^{5}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{x} + \frac{5*-{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{4}x^{2}} + \frac{5({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{2}(2)ln(x)}{(x - 1)^{4}x} + \frac{5 * {2}^{(\frac{ln(x)}{(x - 1)})}*2ln(2)*0ln(x)}{(x - 1)^{4}x(2)} + \frac{5 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{4}x(x)} + \frac{(\frac{-3(1 + 0)}{(x - 1)^{4}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{x^{2}} + \frac{-2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{3}x^{3}} + \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{2}(2)ln(x)}{(x - 1)^{3}x^{2}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*2ln(2)*0ln(x)}{(x - 1)^{3}x^{2}(2)} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{3}x^{2}(x)} - (\frac{-6(1 + 0)}{(x - 1)^{7}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{3}(x) - \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{3}(2)ln^{3}(x)}{(x - 1)^{6}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*3ln^{2}(2)*0ln^{3}(x)}{(x - 1)^{6}(2)} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)*3ln^{2}(x)}{(x - 1)^{6}(x)} + \frac{(\frac{-5(1 + 0)}{(x - 1)^{6}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{2}(x)}{x} + \frac{-{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{2}(x)}{(x - 1)^{5}x^{2}} + \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{3}(2)ln^{2}(x)}{(x - 1)^{5}x} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*3ln^{2}(2)*0ln^{2}(x)}{(x - 1)^{5}x(2)} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)*2ln(x)}{(x - 1)^{5}x(x)} + \frac{7(\frac{-4(1 + 0)}{(x - 1)^{5}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{x} + \frac{7*-{2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{4}x^{2}} + \frac{7({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(x)ln^{2}(2)}{(x - 1)^{4}x} + \frac{7 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{4}x(x)} + \frac{7 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)*2ln(2)*0}{(x - 1)^{4}x(2)} + \frac{2(\frac{-3(1 + 0)}{(x - 1)^{4}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{x^{2}} + \frac{2*-2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{3}x^{3}} + \frac{2({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(x)ln^{2}(2)}{(x - 1)^{3}x^{2}} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{3}x^{2}(x)} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)*2ln(2)*0}{(x - 1)^{3}x^{2}(2)} + \frac{2(\frac{-5(1 + 0)}{(x - 1)^{6}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(x)ln^{3}(2)}{x} + \frac{2*-{2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(x)ln^{3}(2)}{(x - 1)^{5}x^{2}} + \frac{2({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{2}(x)ln^{3}(2)}{(x - 1)^{5}x} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}*2ln(x)ln^{3}(2)}{(x - 1)^{5}x(x)} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(x)*3ln^{2}(2)*0}{(x - 1)^{5}x(2)} - \frac{2(\frac{-4(1 + 0)}{(x - 1)^{5}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln(x)}{x^{2}} - \frac{2*-2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln(x)}{(x - 1)^{4}x^{3}} - \frac{2({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{3}(2)ln(x)}{(x - 1)^{4}x^{2}} - \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}*3ln^{2}(2)*0ln(x)}{(x - 1)^{4}x^{2}(2)} - \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)}{(x - 1)^{4}x^{2}(x)} - \frac{(\frac{-4(1 + 0)}{(x - 1)^{5}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{3}(2)}{x^{2}} - \frac{-2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{3}(2)}{(x - 1)^{4}x^{3}} - \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(x)ln^{3}(2)}{(x - 1)^{4}x^{2}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)}{(x - 1)^{4}x^{2}(x)} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(x)*3ln^{2}(2)*0}{(x - 1)^{4}x^{2}(2)} + \frac{6(\frac{-3(1 + 0)}{(x - 1)^{4}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{x} + \frac{6*-{2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{3}x^{2}} + \frac{6({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(2)}{(x - 1)^{3}x} + \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}*0}{(x - 1)^{3}x(2)} + \frac{3(\frac{-2(1 + 0)}{(x - 1)^{3}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{x^{2}} + \frac{3*-2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{2}x^{3}} + \frac{3({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(2)}{(x - 1)^{2}x^{2}} + \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}*0}{(x - 1)^{2}x^{2}(2)} + \frac{2(\frac{-(1 + 0)}{(x - 1)^{2}}){2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{x^{3}} + \frac{2*-3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x^{4}} + \frac{2({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln(2)}{(x - 1)x^{3}} + \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}*0}{(x - 1)x^{3}(2)} - \frac{3(\frac{-2(1 + 0)}{(x - 1)^{3}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{x^{3}} - \frac{3*-3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{2}x^{4}} - \frac{3({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{2}(2)}{(x - 1)^{2}x^{3}} - \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}*2ln(2)*0}{(x - 1)^{2}x^{3}(2)} - \frac{6(\frac{-3(1 + 0)}{(x - 1)^{4}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{x^{2}} - \frac{6*-2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{3}x^{3}} - \frac{6({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{2}(2)}{(x - 1)^{3}x^{2}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}*2ln(2)*0}{(x - 1)^{3}x^{2}(2)} + \frac{(\frac{-3(1 + 0)}{(x - 1)^{4}}){2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)}{x^{3}} + \frac{-3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)}{(x - 1)^{3}x^{4}} + \frac{({2}^{(\frac{ln(x)}{(x - 1)})}(((\frac{-(1 + 0)}{(x - 1)^{2}})ln(x) + \frac{1}{(x - 1)(x)})ln(2) + \frac{(\frac{ln(x)}{(x - 1)})(0)}{(2)}))ln^{3}(2)}{(x - 1)^{3}x^{3}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}*3ln^{2}(2)*0}{(x - 1)^{3}x^{3}(2)}\\=&\frac{24 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)ln(x)}{(x - 1)^{5}} + \frac{36 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln^{2}(x)}{(x - 1)^{6}} - \frac{26 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{5}x} - \frac{8 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{4}x^{2}} + \frac{12 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{3}(x)}{(x - 1)^{7}} - \frac{11 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{2}(x)}{(x - 1)^{6}x} - \frac{46 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{5}x} - \frac{16 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{4}x^{2}} - \frac{25 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(x)ln^{3}(2)}{(x - 1)^{6}x} + \frac{20 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln(x)}{(x - 1)^{5}x^{2}} + \frac{7 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln(x)}{(x - 1)^{4}x^{3}} - \frac{2 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)ln(x)}{(x - 1)^{3}x^{3}} - \frac{5 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(x)ln^{3}(2)}{(x - 1)^{5}x^{2}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{2}(2)}{(x - 1)^{3}x^{3}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{4}(2)ln^{4}(x)}{(x - 1)^{8}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{4}(2)ln^{3}(x)}{(x - 1)^{7}x} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)ln^{2}(x)}{(x - 1)^{5}x^{2}} - \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(x)ln^{4}(2)}{(x - 1)^{7}x} + \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{4}(2)ln^{2}(x)}{(x - 1)^{6}x^{2}} + \frac{16 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{3}(2)}{(x - 1)^{5}x^{2}} + \frac{5 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{3}(2)}{(x - 1)^{4}x^{3}} + \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(x)ln^{4}(2)}{(x - 1)^{6}x^{2}} - \frac{3 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{4}(2)ln(x)}{(x - 1)^{5}x^{3}} - \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln(x)ln^{4}(2)}{(x - 1)^{5}x^{3}} + \frac{36 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{4}x^{2}} - \frac{12 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)}{(x - 1)^{4}x^{3}} - \frac{24 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{4}x} - \frac{12 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{3}x^{2}} - \frac{8 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)^{2}x^{3}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln(2)}{(x - 1)x^{4}} + \frac{11 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{2}x^{4}} - \frac{6 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{3}(2)}{(x - 1)^{3}x^{4}} + \frac{24 * {2}^{(\frac{ln(x)}{(x - 1)})}ln^{2}(2)}{(x - 1)^{3}x^{3}} + \frac{{2}^{(\frac{ln(x)}{(x - 1)})}ln^{4}(2)}{(x - 1)^{4}x^{4}}\\ \end{split}\end{equation} \]