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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{x}{({x}^{{2}^{{x}^{2}}})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x{x}^{(-{2}^{x^{2}})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x{x}^{(-{2}^{x^{2}})}\right)}{dx}\\=&{x}^{(-{2}^{x^{2}})} + x({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))\\=&-{2}^{x^{2}}{x}^{(-{2}^{x^{2}})} - 2x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) + {x}^{(-{2}^{x^{2}})}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( -{2}^{x^{2}}{x}^{(-{2}^{x^{2}})} - 2x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) + {x}^{(-{2}^{x^{2}})}\right)}{dx}\\=&-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})} - {2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)})) - 2*2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 2x^{2}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 2x^{2}{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(2)ln(x) - \frac{2x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}*0ln(x)}{(2)} - \frac{2x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} + ({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))\\=&4x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4x^{3}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) + 4x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) - 2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 2x{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln(2) - 2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2) + \frac{{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}}{x} - \frac{{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}}{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 4x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4x^{3}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) + 4x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) - 2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 2x{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln(2) - 2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2) + \frac{{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}}{x} - \frac{{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}}{x}\right)}{dx}\\=&4 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) + 4x({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(2)ln(x) + 4x{2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(2)ln(x) + \frac{4x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}*0ln(x)}{(2)} + \frac{4x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} - 4 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4x({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4x{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(2)ln(x) - \frac{4x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}*0ln(x)}{(2)} - \frac{4x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} - 4*3x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) - 4x^{3}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) - 4x^{3}{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{2}(2)ln(x) - \frac{4x^{3}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}*2ln(2)*0ln(x)}{(2)} - \frac{4x^{3}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2)}{(x)} + 4*3x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) + 4x^{3}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) + 4x^{3}{2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{2}(x)ln^{2}(2) + \frac{4x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}*2ln(x)ln^{2}(2)}{(x)} + \frac{4x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)*2ln(2)*0}{(2)} - 2 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 2x({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 2x{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(x)ln(2) - \frac{2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} - \frac{2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(x)*0}{(2)} - 2{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln(2) - 2x({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)})){2}^{x^{2}}ln(2) - 2x{x}^{(-{2}^{x^{2}})}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)}))ln(2) - \frac{2x{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}*0}{(2)} - 2 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2) - 2x({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(2) - 2x{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(2) - \frac{2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}*0}{(2)} + \frac{-{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}}{x^{2}} + \frac{({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}}{x} + \frac{{2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))}{x} - \frac{-{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}}{x^{2}} - \frac{({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}}{x} - \frac{{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))}{x}\\=&8 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) + 20x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) - 12x^{2}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) - 4 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 2 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 24x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) + 24x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) + 4 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 8x^{4}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln(x) + 8x^{4}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{3}(2) + 16x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln^{2}(2) + 16x^{4}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln^{2}(x) - 8x^{4}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(x)ln^{3}(2) - 2 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 8{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln(2) - 4x^{2}{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln^{2}(2) + 8 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2) - 8x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2) - 4 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2) + 4{x}^{(-{2}^{x^{2}})}{2}^{(2x^{2})}ln(2) - \frac{{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}}{x^{2}} + \frac{{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}}{x^{2}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 8 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) + 20x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) - 12x^{2}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) - 4 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 2 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 24x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) + 24x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) + 4 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 8x^{4}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln(x) + 8x^{4}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{3}(2) + 16x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln^{2}(2) + 16x^{4}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln^{2}(x) - 8x^{4}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(x)ln^{3}(2) - 2 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 8{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln(2) - 4x^{2}{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln^{2}(2) + 8 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2) - 8x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2) - 4 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2) + 4{x}^{(-{2}^{x^{2}})}{2}^{(2x^{2})}ln(2) - \frac{{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}}{x^{2}} + \frac{{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}}{x^{2}}\right)}{dx}\\=&8({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(2)ln(x) + 8 * {2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(2)ln(x) + \frac{8 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}*0ln(x)}{(2)} + \frac{8 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} + 20*2x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) + 20x^{2}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) + 20x^{2}{2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{2}(2)ln(x) + \frac{20x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}*2ln(2)*0ln(x)}{(2)} + \frac{20x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)}{(x)} - 12*2x{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) - 12x^{2}({2}^{(3x^{2})}((3*2x)ln(2) + \frac{(3x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) - 12x^{2}{2}^{(3x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{2}(x)ln^{2}(2) - \frac{12x^{2}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}*2ln(x)ln^{2}(2)}{(x)} - \frac{12x^{2}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)*2ln(2)*0}{(2)} - 4({2}^{(3x^{2})}((3*2x)ln(2) + \frac{(3x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4 * {2}^{(3x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(2)ln(x) - \frac{4 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}*0ln(x)}{(2)} - \frac{4 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} - 4({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(2)ln(x) - 4 * {2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(2)ln(x) - \frac{4 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}*0ln(x)}{(2)} - \frac{4 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} - 2({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 2 * {2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(x)ln(2) - \frac{2 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} - \frac{2 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(x)*0}{(2)} - 24*2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) - 24x^{2}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) - 24x^{2}{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{2}(2)ln(x) - \frac{24x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}*2ln(2)*0ln(x)}{(2)} - \frac{24x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2)}{(x)} + 24*2x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) + 24x^{2}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) + 24x^{2}{2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{2}(x)ln^{2}(2) + \frac{24x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}*2ln(x)ln^{2}(2)}{(x)} + \frac{24x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)*2ln(2)*0}{(2)} + 4({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(x)ln(2) + 4 * {2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(x)ln(2) + \frac{4 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} + \frac{4 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)*0}{(2)} - 8*4x^{3}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln(x) - 8x^{4}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{3}(2)ln(x) - 8x^{4}{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{3}(2)ln(x) - \frac{8x^{4}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}*3ln^{2}(2)*0ln(x)}{(2)} - \frac{8x^{4}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{3}(2)}{(x)} + 8*4x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{3}(2) + 8x^{4}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{3}(2) + 8x^{4}{2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{2}(x)ln^{3}(2) + \frac{8x^{4}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}*2ln(x)ln^{3}(2)}{(x)} + \frac{8x^{4}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)*3ln^{2}(2)*0}{(2)} + 16*2x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln^{2}(2) + 16x^{2}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(x)ln^{2}(2) + 16x^{2}{2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(x)ln^{2}(2) + \frac{16x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)}{(x)} + \frac{16x^{2}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)*2ln(2)*0}{(2)} + 16*4x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln^{2}(x) + 16x^{4}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{3}(2)ln^{2}(x) + 16x^{4}{2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{3}(2)ln^{2}(x) + \frac{16x^{4}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}*3ln^{2}(2)*0ln^{2}(x)}{(2)} + \frac{16x^{4}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(2)*2ln(x)}{(x)} - 8*4x^{3}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(x)ln^{3}(2) - 8x^{4}({2}^{(3x^{2})}((3*2x)ln(2) + \frac{(3x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{3}(x)ln^{3}(2) - 8x^{4}{2}^{(3x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{3}(x)ln^{3}(2) - \frac{8x^{4}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}*3ln^{2}(x)ln^{3}(2)}{(x)} - \frac{8x^{4}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(x)*3ln^{2}(2)*0}{(2)} - 2({2}^{(3x^{2})}((3*2x)ln(2) + \frac{(3x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(x)ln(2) - 2 * {2}^{(3x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(x)ln(2) - \frac{2 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)}{(x)} - \frac{2 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)*0}{(2)} - 8({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)})){2}^{x^{2}}ln(2) - 8{x}^{(-{2}^{x^{2}})}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)}))ln(2) - \frac{8{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}*0}{(2)} - 4*2x{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln^{2}(2) - 4x^{2}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)})){2}^{x^{2}}ln^{2}(2) - 4x^{2}{x}^{(-{2}^{x^{2}})}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)}))ln^{2}(2) - \frac{4x^{2}{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}*2ln(2)*0}{(2)} + 8({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(2) + 8 * {2}^{(2x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(2) + \frac{8 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}*0}{(2)} - 8*2x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2) - 8x^{2}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln^{2}(2) - 8x^{2}{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln^{2}(2) - \frac{8x^{2}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}*2ln(2)*0}{(2)} - 4({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}ln(2) - 4 * {2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))ln(2) - \frac{4 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}*0}{(2)} + 4({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)})){2}^{(2x^{2})}ln(2) + 4{x}^{(-{2}^{x^{2}})}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)}))ln(2) + \frac{4{x}^{(-{2}^{x^{2}})}{2}^{(2x^{2})}*0}{(2)} - \frac{-2 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}}{x^{3}} - \frac{({2}^{(3x^{2})}((3*2x)ln(2) + \frac{(3x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}}{x^{2}} - \frac{{2}^{(3x^{2})}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))}{x^{2}} + \frac{-2 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}}{x^{3}} + \frac{({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){x}^{(-{2}^{x^{2}})}}{x^{2}} + \frac{{2}^{x^{2}}({x}^{(-{2}^{x^{2}})}((-({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(x) + \frac{(-{2}^{x^{2}})(1)}{(x)}))}{x^{2}}\\=&136x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) - 24x{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln^{2}(x) - \frac{8 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x)}{x} - 48x{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) + 152x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln(x) - 104x^{3}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{3}(2) - 80x{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) - 40x{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln^{2}(2) - 60x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln(x) - 88x^{3}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln^{2}(x) + 32x^{3}{2}^{(4x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(x)ln^{3}(2) + 12x{2}^{(4x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) + 48x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{2}(2) + 12x{2}^{(4x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln^{2}(x) + \frac{4 * {2}^{(4x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x)}{x} + 80x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln^{2}(2) + 12x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2)ln^{2}(x) + \frac{4 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)ln(x)}{x} - 80x^{3}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln(x) + 80x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{3}(2) + 72x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln^{3}(2) + 160x^{3}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(2)ln^{2}(x) - 80x^{3}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(x)ln^{3}(2) - \frac{4 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln(2)}{x} - 16x^{5}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{4}(2)ln(x) + 16x^{5}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(x)ln^{4}(2) + 96x^{5}{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{4}(2)ln^{2}(x) - 48x^{5}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{3}(x)ln^{4}(2) - 48x^{5}{2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln^{4}(2)ln^{3}(x) + 16x^{5}{2}^{(4x^{2})}{x}^{(-{2}^{x^{2}})}ln^{4}(x)ln^{4}(2) + \frac{4 * {2}^{(4x^{2})}{x}^{(-{2}^{x^{2}})}ln(x)ln(2)}{x} - \frac{6{x}^{(-{2}^{x^{2}})}{2}^{(3x^{2})}ln(2)}{x} - 8x^{3}{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln^{3}(2) + \frac{12{x}^{(-{2}^{x^{2}})}{2}^{(2x^{2})}ln(2)}{x} - \frac{6{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln(2)}{x} - 32x{x}^{(-{2}^{x^{2}})}{2}^{x^{2}}ln^{2}(2) + \frac{12 * {2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)}{x} - 40x{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{2}(2) + 36x{x}^{(-{2}^{x^{2}})}{2}^{(2x^{2})}ln^{2}(2) + 60x{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}ln^{2}(2) - 24x^{3}{2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln^{3}(2) - \frac{18 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}ln(2)}{x} + \frac{2 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}ln(2)}{x} + \frac{{2}^{(4x^{2})}{x}^{(-{2}^{x^{2}})}}{x^{3}} - \frac{2 * {2}^{x^{2}}{x}^{(-{2}^{x^{2}})}}{x^{3}} + \frac{2 * {2}^{(3x^{2})}{x}^{(-{2}^{x^{2}})}}{x^{3}} - \frac{{2}^{(2x^{2})}{x}^{(-{2}^{x^{2}})}}{x^{3}}\\ \end{split}\end{equation} \]