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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{{x}^{(xx + 1)}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{{x}^{(x^{2} + 1)}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{{x}^{(x^{2} + 1)}}\right)}{dx}\\=&e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))\\=&2x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + \frac{{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + \frac{{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{x}\right)}{dx}\\=&2{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 2x({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x) + 2x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x) + \frac{2x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{(x)} + {x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + x({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}} + x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)})) + \frac{-{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{x^{2}} + \frac{({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}}{x} + \frac{{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))}{x}\\=&6{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 4x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 4x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 4x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 4x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + 4{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + 5{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + 2{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + \frac{{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 6{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 4x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 4x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 4x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 4x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + 4{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + 5{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + 2{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + \frac{{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x^{2}}\right)}{dx}\\=&6({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x) + 6{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x) + \frac{6{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{(x)} + 4*2x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 4x^{2}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 4x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln^{2}(x) + \frac{4x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}*2ln(x)}{(x)} + 4*2x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 4x^{2}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x) + 4x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x) + \frac{4x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{(x)} + 4*2x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 4x^{2}({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 4x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln^{2}(x) + \frac{4x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}*2ln(x)}{(x)} + 4*2x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + 4x^{2}({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x) + 4x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x) + \frac{4x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{(x)} + 4({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x) + 4{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x) + \frac{4{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{(x)} + 5({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}} + 5{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)})) + 2x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + x^{2}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}} + x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)})) + 2x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + x^{2}({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}} + x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)})) + 2({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}} + 2{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)})) + \frac{-2{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x^{3}} + \frac{({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}}{x^{2}} + \frac{{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))}{x^{2}}\\=&24x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 36x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + \frac{6{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x)}{x} + 60x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 72x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + \frac{24{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x)}{x} + 8x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 12x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 32x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 48x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 6x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 24x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + \frac{11{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{x} + 21x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + 12x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + \frac{18{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x} + x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + 4x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + \frac{{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 24x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 36x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + \frac{6{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x)}{x} + 60x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 72x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + \frac{24{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x)}{x} + 8x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 12x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 32x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 48x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 6x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 24x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + \frac{11{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{x} + 21x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + 12x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + \frac{18{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x} + x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + 4x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + \frac{{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x^{3}}\right)}{dx}\\=&24{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 24x({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 24x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln^{2}(x) + \frac{24x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}*2ln(x)}{(x)} + 36{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 36x({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x) + 36x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x) + \frac{36x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{(x)} + \frac{6*-{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x)}{x^{2}} + \frac{6({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x)}{x} + \frac{6{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x)}{x} + \frac{6{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{x(x)} + 60{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 60x({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 60x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln^{2}(x) + \frac{60x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}*2ln(x)}{(x)} + 72{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + 72x({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x) + 72x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x) + \frac{72x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{(x)} + \frac{24*-{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x)}{x^{2}} + \frac{24({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x)}{x} + \frac{24{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x)}{x} + \frac{24{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x(x)} + 8*3x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 8x^{3}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 8x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln^{3}(x) + \frac{8x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}*3ln^{2}(x)}{(x)} + 12*3x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 12x^{3}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 12x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln^{2}(x) + \frac{12x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}*2ln(x)}{(x)} + 32*3x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 32x^{3}({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 32x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln^{3}(x) + \frac{32x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}*3ln^{2}(x)}{(x)} + 48*3x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 48x^{3}({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 48x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln^{2}(x) + \frac{48x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}*2ln(x)}{(x)} + 6*3x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 6x^{3}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x) + 6x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x) + \frac{6x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{(x)} + 24*3x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + 24x^{3}({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}ln(x) + 24x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))ln(x) + \frac{24x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{(x)} + \frac{11*-{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{x^{2}} + \frac{11({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}}{x} + \frac{11{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))}{x} + 21{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + 21x({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}} + 21x{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)})) + 12{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + 12x({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}} + 12x{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)})) + \frac{18*-{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x^{2}} + \frac{18({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}}{x} + \frac{18{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))}{x} + 3x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + x^{3}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}} + x^{3}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)})) + 4*3x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + 4x^{3}({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}} + 4x^{3}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)})) + \frac{-3{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x^{4}} + \frac{({x}^{(2x^{2} + 2)}((2*2x + 0)ln(x) + \frac{(2x^{2} + 2)(1)}{(x)}))e^{{x}^{(x^{2} + 1)}}}{x^{3}} + \frac{{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}({x}^{(x^{2} + 1)}((2x + 0)ln(x) + \frac{(x^{2} + 1)(1)}{(x)}))}{x^{3}}\\=&60{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 80x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 168x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 608x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 1104x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 420{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 148{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 108x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 648x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + 652{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + \frac{60{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x)}{x^{2}} + 71{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + 233{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + 16x^{4}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{4}(x) + 32x^{4}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 208x^{4}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{4}(x) + 416x^{4}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{3}(x) + 24x^{4}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 312x^{4}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln^{2}(x) + 8x^{4}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}ln(x) + 104x^{4}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}ln(x) + \frac{74{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}}{x^{2}} + 22x^{2}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + \frac{6{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}}}{x^{2}} + 124x^{2}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}} + x^{4}{x}^{(x^{2} + 1)}e^{{x}^{(x^{2} + 1)}} + 13x^{4}{x}^{(2x^{2} + 2)}e^{{x}^{(x^{2} + 1)}}\\ \end{split}\end{equation} \]