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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (\frac{{2}^{x}}{(ln(2)x)} - {2}^{x}ln(x)){\frac{1}{(log_{2}^{x})}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{2}^{x}}{x{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}ln(x)}{{\left(log(2, x)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{2}^{x}}{x{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}ln(x)}{{\left(log(2, x)^{2}}\right)}{dx}\\=&\frac{-{2}^{x}}{x^{2}{\left(log(2, x)^{2}ln(2)} + \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x{\left(log(2, x)^{2}ln(2)} + \frac{{2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{xln(2)} + \frac{{2}^{x}*-0}{x{\left(log(2, x)^{2}ln^{2}(2)(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{{\left(log(2, x)^{2}} - {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln(x) - \frac{{2}^{x}}{{\left(log(2, x)^{2}(x)}\\=&\frac{2 * {2}^{x}ln(x)}{x{\left(log(2, x)^{3}ln(2)} - \frac{2 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{{2}^{x}ln(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{{2}^{x}}{x^{2}{\left(log(2, x)^{2}ln(2)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2 * {2}^{x}ln(x)}{x{\left(log(2, x)^{3}ln(2)} - \frac{2 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{{2}^{x}ln(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{{2}^{x}}{x^{2}{\left(log(2, x)^{2}ln(2)}\right)}{dx}\\=&\frac{2*-{2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}ln(2)} + \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x{\left(log(2, x)^{3}ln(2)} + \frac{2 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{xln(2)} + \frac{2 * {2}^{x}*-0ln(x)}{x{\left(log(2, x)^{3}ln^{2}(2)(2)} + \frac{2 * {2}^{x}}{x{\left(log(2, x)^{3}ln(2)(x)} - \frac{2*-2 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{2}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{2 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{2}ln^{2}(2)} - \frac{2 * {2}^{x}*-2*0}{x^{2}{\left(log(2, x)^{3}ln^{3}(2)(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)ln(x)}{{\left(log(2, x)^{2}} - {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln(2)ln(x) - \frac{{2}^{x}*0ln(x)}{{\left(log(2, x)^{2}(2)} - \frac{{2}^{x}ln(2)}{{\left(log(2, x)^{2}(x)} - \frac{-2 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}ln(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{2}{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{2}ln(2)} - \frac{{2}^{x}*-0}{x^{2}{\left(log(2, x)^{2}ln^{2}(2)(2)}\\=&\frac{-2 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}ln(2)} - \frac{6 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{4 * {2}^{x}ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{{2}^{x}ln^{2}(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{{2}^{x}ln(2)}{x{\left(log(2, x)^{2}} + \frac{2 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}}{x^{2}{\left(log(2, x)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}ln(2)} - \frac{6 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{4 * {2}^{x}ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{{2}^{x}ln^{2}(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{{2}^{x}ln(2)}{x{\left(log(2, x)^{2}} + \frac{2 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}}{x^{2}{\left(log(2, x)^{2}}\right)}{dx}\\=&\frac{-2*-2 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}ln(2)} - \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{2}{\left(log(2, x)^{3}ln(2)} - \frac{2 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{x^{2}ln(2)} - \frac{2 * {2}^{x}*-0ln(x)}{x^{2}{\left(log(2, x)^{3}ln^{2}(2)(2)} - \frac{2 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}ln(2)(x)} - \frac{6*-2 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{6 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})ln(x)}{x^{2}ln^{2}(2)} - \frac{6 * {2}^{x}*-2*0ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{3}(2)(2)} - \frac{6 * {2}^{x}}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)(x)} + \frac{4*-{2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}} + \frac{4({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x{\left(log(2, x)^{3}} + \frac{4 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{x} + \frac{4 * {2}^{x}}{x{\left(log(2, x)^{3}(x)} + \frac{6*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{3}ln^{2}(2)} + \frac{6 * {2}^{x}*-2*0}{x^{3}{\left(log(2, x)^{3}ln^{3}(2)(2)} + \frac{6*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{4}ln^{3}(2)} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{4}ln^{3}(2)} + \frac{6 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})}{x^{3}ln^{3}(2)} + \frac{6 * {2}^{x}*-3*0}{x^{3}{\left(log(2, x)^{4}ln^{4}(2)(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln^{2}(2)ln(x)}{{\left(log(2, x)^{2}} - {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln^{2}(2)ln(x) - \frac{{2}^{x}*2ln(2)*0ln(x)}{{\left(log(2, x)^{2}(2)} - \frac{{2}^{x}ln^{2}(2)}{{\left(log(2, x)^{2}(x)} - \frac{-{2}^{x}ln(2)}{x^{2}{\left(log(2, x)^{2}} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)}{x{\left(log(2, x)^{2}} - \frac{{2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln(2)}{x} - \frac{{2}^{x}*0}{x{\left(log(2, x)^{2}(2)} + \frac{2*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}ln(2)} + \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{2}ln(2)} + \frac{2 * {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{3}ln(2)} + \frac{2 * {2}^{x}*-0}{x^{3}{\left(log(2, x)^{2}ln^{2}(2)(2)} - \frac{-2 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{2}{\left(log(2, x)^{2}} - \frac{{2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{2}}\\=&\frac{4 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}ln(2)} + \frac{18 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{18 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}ln(2)} + \frac{24 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{3}(2)} + \frac{6 * {2}^{x}ln(2)ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln(2)} - \frac{6 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}} - \frac{22 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{36 * {2}^{x}}{x^{4}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{2 * {2}^{x}ln^{2}(2)}{x{\left(log(2, x)^{2}} - \frac{24 * {2}^{x}}{x^{4}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{{2}^{x}ln^{3}(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{6 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}ln(2)} + \frac{6 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}} + \frac{4 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{4 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}ln(2)} + \frac{18 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{18 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}ln(2)} + \frac{24 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{3}(2)} + \frac{6 * {2}^{x}ln(2)ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln(2)} - \frac{6 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}} - \frac{22 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{36 * {2}^{x}}{x^{4}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{2 * {2}^{x}ln^{2}(2)}{x{\left(log(2, x)^{2}} - \frac{24 * {2}^{x}}{x^{4}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{{2}^{x}ln^{3}(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{6 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}ln(2)} + \frac{6 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}} + \frac{4 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}}\right)}{dx}\\=&\frac{4*-3 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{3}ln(2)} + \frac{4({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{3}{\left(log(2, x)^{3}ln(2)} + \frac{4 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{x^{3}ln(2)} + \frac{4 * {2}^{x}*-0ln(x)}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)(2)} + \frac{4 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln(2)(x)} + \frac{18*-3 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{18({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{18 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})ln(x)}{x^{3}ln^{2}(2)} + \frac{18 * {2}^{x}*-2*0ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{3}(2)(2)} + \frac{18 * {2}^{x}}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)(x)} - \frac{18*-2 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln(2)} - \frac{18({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{2}{\left(log(2, x)^{4}ln(2)} - \frac{18 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})ln(x)}{x^{2}ln(2)} - \frac{18 * {2}^{x}*-0ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)(2)} - \frac{18 * {2}^{x}}{x^{2}{\left(log(2, x)^{4}ln(2)(x)} + \frac{24*-3 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{5}ln^{3}(2)} + \frac{24({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{3}(2)} + \frac{24 * {2}^{x}(\frac{-5(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{6}(ln(2))})ln(x)}{x^{3}ln^{3}(2)} + \frac{24 * {2}^{x}*-3*0ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{4}(2)(2)} + \frac{24 * {2}^{x}}{x^{3}{\left(log(2, x)^{5}ln^{3}(2)(x)} + \frac{6*-{2}^{x}ln(2)ln(x)}{x^{2}{\left(log(2, x)^{3}} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(2)ln(x)}{x} + \frac{6 * {2}^{x}*0ln(x)}{x{\left(log(2, x)^{3}(2)} + \frac{6 * {2}^{x}ln(2)}{x{\left(log(2, x)^{3}(x)} + \frac{6*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln(2)} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{3}ln(2)} + \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{3}ln(2)} + \frac{6 * {2}^{x}*-0}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)(2)} - \frac{6*-2 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}} - \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{2}{\left(log(2, x)^{3}} - \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{x^{2}} - \frac{6 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}(x)} - \frac{22*-4 * {2}^{x}}{x^{5}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{22({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{4}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{22 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{4}ln^{2}(2)} - \frac{22 * {2}^{x}*-2*0}{x^{4}{\left(log(2, x)^{3}ln^{3}(2)(2)} - \frac{36*-4 * {2}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{36({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{4}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{36 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})}{x^{4}ln^{3}(2)} - \frac{36 * {2}^{x}*-3*0}{x^{4}{\left(log(2, x)^{4}ln^{4}(2)(2)} - \frac{2*-{2}^{x}ln^{2}(2)}{x^{2}{\left(log(2, x)^{2}} - \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln^{2}(2)}{x{\left(log(2, x)^{2}} - \frac{2 * {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln^{2}(2)}{x} - \frac{2 * {2}^{x}*2ln(2)*0}{x{\left(log(2, x)^{2}(2)} - \frac{24*-4 * {2}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{24({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{4}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{24 * {2}^{x}(\frac{-5(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{6}(ln(2))})}{x^{4}ln^{4}(2)} - \frac{24 * {2}^{x}*-4*0}{x^{4}{\left(log(2, x)^{5}ln^{5}(2)(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln^{3}(2)ln(x)}{{\left(log(2, x)^{2}} - {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln^{3}(2)ln(x) - \frac{{2}^{x}*3ln^{2}(2)*0ln(x)}{{\left(log(2, x)^{2}(2)} - \frac{{2}^{x}ln^{3}(2)}{{\left(log(2, x)^{2}(x)} - \frac{6*-4 * {2}^{x}}{x^{5}{\left(log(2, x)^{2}ln(2)} - \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{4}{\left(log(2, x)^{2}ln(2)} - \frac{6 * {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{4}ln(2)} - \frac{6 * {2}^{x}*-0}{x^{4}{\left(log(2, x)^{2}ln^{2}(2)(2)} + \frac{6*-2 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{2}{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{2}} + \frac{4*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}} + \frac{4({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{2}} + \frac{4 * {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{3}}\\=&\frac{-12 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{3}ln(2)} - \frac{66 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{72 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln(2)} - \frac{144 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{5}ln^{3}(2)} - \frac{12 * {2}^{x}ln(2)ln(x)}{x^{2}{\left(log(2, x)^{3}} + \frac{96 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{2}(2)} - \frac{120 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{6}ln^{4}(2)} + \frac{8 * {2}^{x}ln^{2}(2)ln(x)}{x{\left(log(2, x)^{3}} - \frac{36 * {2}^{x}}{x^{3}{\left(log(2, x)^{4}ln(2)} - \frac{36 * {2}^{x}}{x^{4}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{36 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}} - \frac{44 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln(2)} + \frac{16 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}} + \frac{16 * {2}^{x}ln(2)}{x^{2}{\left(log(2, x)^{3}} + \frac{100 * {2}^{x}}{x^{5}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{210 * {2}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{3}(2)} + \frac{2 * {2}^{x}ln^{2}(2)}{x^{2}{\left(log(2, x)^{2}} + \frac{240 * {2}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{3 * {2}^{x}ln^{3}(2)}{x{\left(log(2, x)^{2}} + \frac{120 * {2}^{x}}{x^{5}{\left(log(2, x)^{6}ln^{5}(2)} + \frac{24 * {2}^{x}}{x^{5}{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}ln^{4}(2)ln(x)}{{\left(log(2, x)^{2}} + \frac{4 * {2}^{x}ln(2)}{x^{3}{\left(log(2, x)^{2}} - \frac{18 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}} - \frac{12 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}}\\ \end{split}\end{equation} \]
Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ (\frac{{2}^{x}}{(ln(2)x)} - {2}^{x}ln(x)){\frac{1}{(log_{2}^{x})}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{2}^{x}}{x{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}ln(x)}{{\left(log(2, x)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{2}^{x}}{x{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}ln(x)}{{\left(log(2, x)^{2}}\right)}{dx}\\=&\frac{-{2}^{x}}{x^{2}{\left(log(2, x)^{2}ln(2)} + \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x{\left(log(2, x)^{2}ln(2)} + \frac{{2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{xln(2)} + \frac{{2}^{x}*-0}{x{\left(log(2, x)^{2}ln^{2}(2)(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{{\left(log(2, x)^{2}} - {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln(x) - \frac{{2}^{x}}{{\left(log(2, x)^{2}(x)}\\=&\frac{2 * {2}^{x}ln(x)}{x{\left(log(2, x)^{3}ln(2)} - \frac{2 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{{2}^{x}ln(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{{2}^{x}}{x^{2}{\left(log(2, x)^{2}ln(2)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{2 * {2}^{x}ln(x)}{x{\left(log(2, x)^{3}ln(2)} - \frac{2 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{{2}^{x}ln(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{{2}^{x}}{x^{2}{\left(log(2, x)^{2}ln(2)}\right)}{dx}\\=&\frac{2*-{2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}ln(2)} + \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x{\left(log(2, x)^{3}ln(2)} + \frac{2 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{xln(2)} + \frac{2 * {2}^{x}*-0ln(x)}{x{\left(log(2, x)^{3}ln^{2}(2)(2)} + \frac{2 * {2}^{x}}{x{\left(log(2, x)^{3}ln(2)(x)} - \frac{2*-2 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{2}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{2 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{2}ln^{2}(2)} - \frac{2 * {2}^{x}*-2*0}{x^{2}{\left(log(2, x)^{3}ln^{3}(2)(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)ln(x)}{{\left(log(2, x)^{2}} - {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln(2)ln(x) - \frac{{2}^{x}*0ln(x)}{{\left(log(2, x)^{2}(2)} - \frac{{2}^{x}ln(2)}{{\left(log(2, x)^{2}(x)} - \frac{-2 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}ln(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{2}{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{2}ln(2)} - \frac{{2}^{x}*-0}{x^{2}{\left(log(2, x)^{2}ln^{2}(2)(2)}\\=&\frac{-2 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}ln(2)} - \frac{6 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{4 * {2}^{x}ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{{2}^{x}ln^{2}(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{{2}^{x}ln(2)}{x{\left(log(2, x)^{2}} + \frac{2 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}}{x^{2}{\left(log(2, x)^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}ln(2)} - \frac{6 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{4 * {2}^{x}ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{{2}^{x}ln^{2}(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{{2}^{x}ln(2)}{x{\left(log(2, x)^{2}} + \frac{2 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}}{x^{2}{\left(log(2, x)^{2}}\right)}{dx}\\=&\frac{-2*-2 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}ln(2)} - \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{2}{\left(log(2, x)^{3}ln(2)} - \frac{2 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{x^{2}ln(2)} - \frac{2 * {2}^{x}*-0ln(x)}{x^{2}{\left(log(2, x)^{3}ln^{2}(2)(2)} - \frac{2 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}ln(2)(x)} - \frac{6*-2 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{6 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})ln(x)}{x^{2}ln^{2}(2)} - \frac{6 * {2}^{x}*-2*0ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{3}(2)(2)} - \frac{6 * {2}^{x}}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)(x)} + \frac{4*-{2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}} + \frac{4({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x{\left(log(2, x)^{3}} + \frac{4 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{x} + \frac{4 * {2}^{x}}{x{\left(log(2, x)^{3}(x)} + \frac{6*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{3}ln^{2}(2)} + \frac{6 * {2}^{x}*-2*0}{x^{3}{\left(log(2, x)^{3}ln^{3}(2)(2)} + \frac{6*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{4}ln^{3}(2)} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{4}ln^{3}(2)} + \frac{6 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})}{x^{3}ln^{3}(2)} + \frac{6 * {2}^{x}*-3*0}{x^{3}{\left(log(2, x)^{4}ln^{4}(2)(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln^{2}(2)ln(x)}{{\left(log(2, x)^{2}} - {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln^{2}(2)ln(x) - \frac{{2}^{x}*2ln(2)*0ln(x)}{{\left(log(2, x)^{2}(2)} - \frac{{2}^{x}ln^{2}(2)}{{\left(log(2, x)^{2}(x)} - \frac{-{2}^{x}ln(2)}{x^{2}{\left(log(2, x)^{2}} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)}{x{\left(log(2, x)^{2}} - \frac{{2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln(2)}{x} - \frac{{2}^{x}*0}{x{\left(log(2, x)^{2}(2)} + \frac{2*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}ln(2)} + \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{2}ln(2)} + \frac{2 * {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{3}ln(2)} + \frac{2 * {2}^{x}*-0}{x^{3}{\left(log(2, x)^{2}ln^{2}(2)(2)} - \frac{-2 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{2}{\left(log(2, x)^{2}} - \frac{{2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{2}}\\=&\frac{4 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}ln(2)} + \frac{18 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{18 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}ln(2)} + \frac{24 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{3}(2)} + \frac{6 * {2}^{x}ln(2)ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln(2)} - \frac{6 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}} - \frac{22 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{36 * {2}^{x}}{x^{4}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{2 * {2}^{x}ln^{2}(2)}{x{\left(log(2, x)^{2}} - \frac{24 * {2}^{x}}{x^{4}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{{2}^{x}ln^{3}(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{6 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}ln(2)} + \frac{6 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}} + \frac{4 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{4 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}ln(2)} + \frac{18 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{18 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}ln(2)} + \frac{24 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{3}(2)} + \frac{6 * {2}^{x}ln(2)ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln(2)} - \frac{6 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{3}} - \frac{22 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{36 * {2}^{x}}{x^{4}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{2 * {2}^{x}ln^{2}(2)}{x{\left(log(2, x)^{2}} - \frac{24 * {2}^{x}}{x^{4}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{{2}^{x}ln^{3}(2)ln(x)}{{\left(log(2, x)^{2}} - \frac{6 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}ln(2)} + \frac{6 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}} + \frac{4 * {2}^{x}}{x^{3}{\left(log(2, x)^{2}}\right)}{dx}\\=&\frac{4*-3 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{3}ln(2)} + \frac{4({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{3}{\left(log(2, x)^{3}ln(2)} + \frac{4 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{x^{3}ln(2)} + \frac{4 * {2}^{x}*-0ln(x)}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)(2)} + \frac{4 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}ln(2)(x)} + \frac{18*-3 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{18({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{18 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})ln(x)}{x^{3}ln^{2}(2)} + \frac{18 * {2}^{x}*-2*0ln(x)}{x^{3}{\left(log(2, x)^{4}ln^{3}(2)(2)} + \frac{18 * {2}^{x}}{x^{3}{\left(log(2, x)^{4}ln^{2}(2)(x)} - \frac{18*-2 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln(2)} - \frac{18({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{2}{\left(log(2, x)^{4}ln(2)} - \frac{18 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})ln(x)}{x^{2}ln(2)} - \frac{18 * {2}^{x}*-0ln(x)}{x^{2}{\left(log(2, x)^{4}ln^{2}(2)(2)} - \frac{18 * {2}^{x}}{x^{2}{\left(log(2, x)^{4}ln(2)(x)} + \frac{24*-3 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{5}ln^{3}(2)} + \frac{24({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{3}(2)} + \frac{24 * {2}^{x}(\frac{-5(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{6}(ln(2))})ln(x)}{x^{3}ln^{3}(2)} + \frac{24 * {2}^{x}*-3*0ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{4}(2)(2)} + \frac{24 * {2}^{x}}{x^{3}{\left(log(2, x)^{5}ln^{3}(2)(x)} + \frac{6*-{2}^{x}ln(2)ln(x)}{x^{2}{\left(log(2, x)^{3}} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(2)ln(x)}{x{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(2)ln(x)}{x} + \frac{6 * {2}^{x}*0ln(x)}{x{\left(log(2, x)^{3}(2)} + \frac{6 * {2}^{x}ln(2)}{x{\left(log(2, x)^{3}(x)} + \frac{6*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln(2)} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{3}ln(2)} + \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{3}ln(2)} + \frac{6 * {2}^{x}*-0}{x^{3}{\left(log(2, x)^{3}ln^{2}(2)(2)} - \frac{6*-2 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}} - \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln(x)}{x^{2}{\left(log(2, x)^{3}} - \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})ln(x)}{x^{2}} - \frac{6 * {2}^{x}}{x^{2}{\left(log(2, x)^{3}(x)} - \frac{22*-4 * {2}^{x}}{x^{5}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{22({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{4}{\left(log(2, x)^{3}ln^{2}(2)} - \frac{22 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{4}ln^{2}(2)} - \frac{22 * {2}^{x}*-2*0}{x^{4}{\left(log(2, x)^{3}ln^{3}(2)(2)} - \frac{36*-4 * {2}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{36({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{4}{\left(log(2, x)^{4}ln^{3}(2)} - \frac{36 * {2}^{x}(\frac{-4(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{5}(ln(2))})}{x^{4}ln^{3}(2)} - \frac{36 * {2}^{x}*-3*0}{x^{4}{\left(log(2, x)^{4}ln^{4}(2)(2)} - \frac{2*-{2}^{x}ln^{2}(2)}{x^{2}{\left(log(2, x)^{2}} - \frac{2({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln^{2}(2)}{x{\left(log(2, x)^{2}} - \frac{2 * {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln^{2}(2)}{x} - \frac{2 * {2}^{x}*2ln(2)*0}{x{\left(log(2, x)^{2}(2)} - \frac{24*-4 * {2}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{24({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{4}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{24 * {2}^{x}(\frac{-5(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{6}(ln(2))})}{x^{4}ln^{4}(2)} - \frac{24 * {2}^{x}*-4*0}{x^{4}{\left(log(2, x)^{5}ln^{5}(2)(2)} - \frac{({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))ln^{3}(2)ln(x)}{{\left(log(2, x)^{2}} - {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})ln^{3}(2)ln(x) - \frac{{2}^{x}*3ln^{2}(2)*0ln(x)}{{\left(log(2, x)^{2}(2)} - \frac{{2}^{x}ln^{3}(2)}{{\left(log(2, x)^{2}(x)} - \frac{6*-4 * {2}^{x}}{x^{5}{\left(log(2, x)^{2}ln(2)} - \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{4}{\left(log(2, x)^{2}ln(2)} - \frac{6 * {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{4}ln(2)} - \frac{6 * {2}^{x}*-0}{x^{4}{\left(log(2, x)^{2}ln^{2}(2)(2)} + \frac{6*-2 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}} + \frac{6({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{2}{\left(log(2, x)^{3}} + \frac{6 * {2}^{x}(\frac{-3(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{4}(ln(2))})}{x^{2}} + \frac{4*-3 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}} + \frac{4({2}^{x}((1)ln(2) + \frac{(x)(0)}{(2)}))}{x^{3}{\left(log(2, x)^{2}} + \frac{4 * {2}^{x}(\frac{-2(\frac{(1)}{(x)} - \frac{(0)log_{2}^{x}}{(2)})}{{\left(log(2, x)^{3}(ln(2))})}{x^{3}}\\=&\frac{-12 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{3}ln(2)} - \frac{66 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{4}ln^{2}(2)} + \frac{72 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{4}ln(2)} - \frac{144 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{5}ln^{3}(2)} - \frac{12 * {2}^{x}ln(2)ln(x)}{x^{2}{\left(log(2, x)^{3}} + \frac{96 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{5}ln^{2}(2)} - \frac{120 * {2}^{x}ln(x)}{x^{4}{\left(log(2, x)^{6}ln^{4}(2)} + \frac{8 * {2}^{x}ln^{2}(2)ln(x)}{x{\left(log(2, x)^{3}} - \frac{36 * {2}^{x}}{x^{3}{\left(log(2, x)^{4}ln(2)} - \frac{36 * {2}^{x}}{x^{4}{\left(log(2, x)^{4}ln^{2}(2)} - \frac{36 * {2}^{x}ln(x)}{x^{2}{\left(log(2, x)^{4}} - \frac{44 * {2}^{x}}{x^{4}{\left(log(2, x)^{3}ln(2)} + \frac{16 * {2}^{x}ln(x)}{x^{3}{\left(log(2, x)^{3}} + \frac{16 * {2}^{x}ln(2)}{x^{2}{\left(log(2, x)^{3}} + \frac{100 * {2}^{x}}{x^{5}{\left(log(2, x)^{3}ln^{2}(2)} + \frac{210 * {2}^{x}}{x^{5}{\left(log(2, x)^{4}ln^{3}(2)} + \frac{2 * {2}^{x}ln^{2}(2)}{x^{2}{\left(log(2, x)^{2}} + \frac{240 * {2}^{x}}{x^{5}{\left(log(2, x)^{5}ln^{4}(2)} - \frac{3 * {2}^{x}ln^{3}(2)}{x{\left(log(2, x)^{2}} + \frac{120 * {2}^{x}}{x^{5}{\left(log(2, x)^{6}ln^{5}(2)} + \frac{24 * {2}^{x}}{x^{5}{\left(log(2, x)^{2}ln(2)} - \frac{{2}^{x}ln^{4}(2)ln(x)}{{\left(log(2, x)^{2}} + \frac{4 * {2}^{x}ln(2)}{x^{3}{\left(log(2, x)^{2}} - \frac{18 * {2}^{x}}{x^{4}{\left(log(2, x)^{2}} - \frac{12 * {2}^{x}}{x^{3}{\left(log(2, x)^{3}}\\ \end{split}\end{equation} \]