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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{{(-1)}^{{x}^{n}}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{{-1}^{{x}^{n}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{{-1}^{{x}^{n}}}\right)}{dx}\\=&e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))\\=&\frac{n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x}\right)}{dx}\\=&\frac{n*-{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{2}} + \frac{n({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x} + \frac{n{x}^{n}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln(-1)}{x} + \frac{n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln(-1)}{x} + \frac{n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*0}{x(-1)}\\=&\frac{-n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{2}} + \frac{n^{2}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{2}} + \frac{n^{2}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{2}}\right)}{dx}\\=&\frac{-n*-2{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} - \frac{n({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{2}} - \frac{n{x}^{n}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln(-1)}{x^{2}} - \frac{n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln(-1)}{x^{2}} - \frac{n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*0}{x^{2}(-1)} + \frac{n^{2}*-2{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} + \frac{n^{2}({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{2}} + \frac{n^{2}{x}^{n}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln(-1)}{x^{2}} + \frac{n^{2}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln(-1)}{x^{2}} + \frac{n^{2}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*0}{x^{2}(-1)} + \frac{n^{2}*-2{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{n^{2}({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln^{2}(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*2ln(-1)*0}{x^{2}(-1)} + \frac{n^{2}*-2{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{n^{2}({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)})){-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}({-1}^{(2{x}^{n})}((2({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{(2{x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln^{2}(-1)}{x^{2}} + \frac{n^{2}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}*2ln(-1)*0}{x^{2}(-1)}\\=&\frac{2n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} - \frac{3n^{2}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{n^{3}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(3n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}{-1}^{(3{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{2n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} - \frac{3n^{2}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{n^{3}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(3n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}{-1}^{(3{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}}\right)}{dx}\\=&\frac{2n*-3{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{4}} + \frac{2n({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} + \frac{2n{x}^{n}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} + \frac{2n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln(-1)}{x^{3}} + \frac{2n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*0}{x^{3}(-1)} - \frac{3n^{2}*-3{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{4}} - \frac{3n^{2}({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} - \frac{3n^{2}{x}^{n}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} - \frac{3n^{2}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln(-1)}{x^{3}} - \frac{3n^{2}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*0}{x^{3}(-1)} - \frac{3n^{2}*-3{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} - \frac{3n^{2}({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln^{2}(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*2ln(-1)*0}{x^{3}(-1)} - \frac{3n^{2}*-3{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} - \frac{3n^{2}({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)})){-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}({-1}^{(2{x}^{n})}((2({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{(2{x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln^{2}(-1)}{x^{3}} - \frac{3n^{2}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}*2ln(-1)*0}{x^{3}(-1)} + \frac{n^{3}*-3{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{4}} + \frac{n^{3}({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} + \frac{n^{3}{x}^{n}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln(-1)}{x^{3}} + \frac{n^{3}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln(-1)}{x^{3}} + \frac{n^{3}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*0}{x^{3}(-1)} + \frac{3n^{3}*-3{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} + \frac{3n^{3}({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln^{2}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*2ln(-1)*0}{x^{3}(-1)} + \frac{3n^{3}*-3{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} + \frac{3n^{3}({x}^{(2n)}((0)ln(x) + \frac{(2n)(1)}{(x)})){-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}({-1}^{(2{x}^{n})}((2({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{(2{x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln^{2}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}*2ln(-1)*0}{x^{3}(-1)} + \frac{n^{3}*-3{x}^{(3n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{4}} + \frac{n^{3}({x}^{(3n)}((0)ln(x) + \frac{(3n)(1)}{(x)})){-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln^{3}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}*3ln^{2}(-1)*0}{x^{3}(-1)} + \frac{3n^{3}*-3{x}^{(3n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{4}} + \frac{3n^{3}({x}^{(3n)}((0)ln(x) + \frac{(3n)(1)}{(x)})){-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(3n)}({-1}^{(2{x}^{n})}((2({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{(2{x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(3n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln^{3}(-1)}{x^{3}} + \frac{3n^{3}{x}^{(3n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}*3ln^{2}(-1)*0}{x^{3}(-1)} + \frac{n^{3}*-3{x}^{(3n)}{-1}^{(3{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{4}} + \frac{n^{3}({x}^{(3n)}((0)ln(x) + \frac{(3n)(1)}{(x)})){-1}^{(3{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}({-1}^{(3{x}^{n})}((3({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{(3{x}^{n})(0)}{(-1)}))e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}{-1}^{(3{x}^{n})}e^{{-1}^{{x}^{n}}}({-1}^{{x}^{n}}((({x}^{n}((0)ln(x) + \frac{(n)(1)}{(x)})))ln(-1) + \frac{({x}^{n})(0)}{(-1)}))ln^{3}(-1)}{x^{3}} + \frac{n^{3}{x}^{(3n)}{-1}^{(3{x}^{n})}e^{{-1}^{{x}^{n}}}*3ln^{2}(-1)*0}{x^{3}(-1)}\\=&\frac{-6n{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{4}} + \frac{11n^{2}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{4}} + \frac{11n^{2}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} + \frac{11n^{2}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} - \frac{6n^{3}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{4}} - \frac{18n^{3}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} - \frac{18n^{3}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} - \frac{6n^{3}{x}^{(3n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{4}} - \frac{18n^{3}{x}^{(3n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{4}} - \frac{6n^{3}{x}^{(3n)}{-1}^{(3{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{4}} + \frac{n^{4}{x}^{n}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln(-1)}{x^{4}} + \frac{7n^{4}{x}^{(2n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} + \frac{7n^{4}{x}^{(2n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{2}(-1)}{x^{4}} + \frac{6n^{4}{x}^{(3n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{4}} + \frac{18n^{4}{x}^{(3n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{4}} + \frac{6n^{4}{x}^{(3n)}{-1}^{(3{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{3}(-1)}{x^{4}} + \frac{n^{4}{x}^{(4n)}{-1}^{{x}^{n}}e^{{-1}^{{x}^{n}}}ln^{4}(-1)}{x^{4}} + \frac{7n^{4}{x}^{(4n)}{-1}^{(2{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{4}(-1)}{x^{4}} + \frac{6n^{4}{x}^{(4n)}{-1}^{(3{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{4}(-1)}{x^{4}} + \frac{n^{4}{x}^{(4n)}{-1}^{(4{x}^{n})}e^{{-1}^{{x}^{n}}}ln^{4}(-1)}{x^{4}}\\ \end{split}\end{equation} \]