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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ e^{{a}^{{2}^{{x}^{2}}}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = e^{{a}^{{2}^{x^{2}}}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( e^{{a}^{{2}^{x^{2}}}}\right)}{dx}\\=&e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))\\=&2x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln(2)ln(a)\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 2x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln(2)ln(a)\right)}{dx}\\=&2 * {2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln(2)ln(a) + 2x({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln(2)ln(a) + 2x{2}^{x^{2}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln(2)ln(a) + 2x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln(2)ln(a) + \frac{2x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*0ln(a)}{(2)} + \frac{2x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln(2)*0}{(a)}\\=&2 * {2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln(2)ln(a) + 4x^{2}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 4x^{2}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 4x^{2}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a)\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2 * {2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln(2)ln(a) + 4x^{2}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 4x^{2}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 4x^{2}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a)\right)}{dx}\\=&2({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln(2)ln(a) + 2 * {2}^{x^{2}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln(2)ln(a) + 2 * {2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln(2)ln(a) + \frac{2 * {2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*0ln(a)}{(2)} + \frac{2 * {2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln(2)*0}{(a)} + 4*2x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 4x^{2}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 4x^{2}{2}^{x^{2}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 4x^{2}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{2}(2)ln(a) + \frac{4x^{2}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*2ln(2)*0ln(a)}{(2)} + \frac{4x^{2}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)*0}{(a)} + 4*2x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 4x^{2}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 4x^{2}{2}^{(2x^{2})}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 4x^{2}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{2}(2)ln^{2}(a) + \frac{4x^{2}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*2ln(2)*0ln^{2}(a)}{(2)} + \frac{4x^{2}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)*2ln(a)*0}{(a)} + 4*2x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 4x^{2}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 4x^{2}{2}^{(2x^{2})}({a}^{(2 * {2}^{x^{2}})}((2({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{(2 * {2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 4x^{2}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{2}(2)ln^{2}(a) + \frac{4x^{2}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}*2ln(2)*0ln^{2}(a)}{(2)} + \frac{4x^{2}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)*2ln(a)*0}{(a)}\\=&12x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 4x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 4x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 8x^{3}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln(a) + 24x^{3}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 24x^{3}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 8x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x^{3}{2}^{(3x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 24x^{3}{2}^{(3x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 8x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x^{3}{2}^{(3x^{2})}{a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a)\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 12x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 4x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 4x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 8x^{3}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln(a) + 24x^{3}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 24x^{3}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 8x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x^{3}{2}^{(3x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 24x^{3}{2}^{(3x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 8x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x^{3}{2}^{(3x^{2})}{a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a)\right)}{dx}\\=&12 * {2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 12x({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 12x{2}^{x^{2}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 12x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{2}(2)ln(a) + \frac{12x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*2ln(2)*0ln(a)}{(2)} + \frac{12x{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)*0}{(a)} + 4 * {2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 4x({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 4x{2}^{(2x^{2})}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 4x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{2}(a)ln^{2}(2) + \frac{4x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*2ln(a)*0ln^{2}(2)}{(a)} + \frac{4x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)*2ln(2)*0}{(2)} + 4 * {2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 4x({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 4x{2}^{(2x^{2})}({a}^{(2 * {2}^{x^{2}})}((2({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{(2 * {2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 4x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{2}(a)ln^{2}(2) + \frac{4x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}*2ln(a)*0ln^{2}(2)}{(a)} + \frac{4x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)*2ln(2)*0}{(2)} + 8*3x^{2}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln(a) + 8x^{3}({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln(a) + 8x^{3}{2}^{x^{2}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln(a) + 8x^{3}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{3}(2)ln(a) + \frac{8x^{3}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*3ln^{2}(2)*0ln(a)}{(2)} + \frac{8x^{3}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)*0}{(a)} + 24*3x^{2}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 24x^{3}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 24x^{3}{2}^{(2x^{2})}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 24x^{3}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{3}(2)ln^{2}(a) + \frac{24x^{3}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*3ln^{2}(2)*0ln^{2}(a)}{(2)} + \frac{24x^{3}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)*2ln(a)*0}{(a)} + 24*3x^{2}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 24x^{3}({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 24x^{3}{2}^{(2x^{2})}({a}^{(2 * {2}^{x^{2}})}((2({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{(2 * {2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 24x^{3}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{3}(2)ln^{2}(a) + \frac{24x^{3}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}*3ln^{2}(2)*0ln^{2}(a)}{(2)} + \frac{24x^{3}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)*2ln(a)*0}{(a)} + 8 * {2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x{2}^{(2x^{2})}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{2}(2)ln^{2}(a) + \frac{8x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*2ln(2)*0ln^{2}(a)}{(2)} + \frac{8x{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)*2ln(a)*0}{(a)} + 8*3x^{2}{2}^{(3x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 8x^{3}({2}^{(3x^{2})}((3*2x)ln(2) + \frac{(3x^{2})(0)}{(2)})){a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 8x^{3}{2}^{(3x^{2})}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 8x^{3}{2}^{(3x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{3}(2)ln^{3}(a) + \frac{8x^{3}{2}^{(3x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}*3ln^{2}(2)*0ln^{3}(a)}{(2)} + \frac{8x^{3}{2}^{(3x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)*3ln^{2}(a)*0}{(a)} + 24*3x^{2}{2}^{(3x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 24x^{3}({2}^{(3x^{2})}((3*2x)ln(2) + \frac{(3x^{2})(0)}{(2)})){a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 24x^{3}{2}^{(3x^{2})}({a}^{(2 * {2}^{x^{2}})}((2({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{(2 * {2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 24x^{3}{2}^{(3x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{3}(2)ln^{3}(a) + \frac{24x^{3}{2}^{(3x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}*3ln^{2}(2)*0ln^{3}(a)}{(2)} + \frac{24x^{3}{2}^{(3x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)*3ln^{2}(a)*0}{(a)} + 8 * {2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x({2}^{(2x^{2})}((2*2x)ln(2) + \frac{(2x^{2})(0)}{(2)})){a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x{2}^{(2x^{2})}({a}^{(2 * {2}^{x^{2}})}((2({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{(2 * {2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 8x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{2}(2)ln^{2}(a) + \frac{8x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}*2ln(2)*0ln^{2}(a)}{(2)} + \frac{8x{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)*2ln(a)*0}{(a)} + 8*3x^{2}{2}^{(3x^{2})}{a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 8x^{3}({2}^{(3x^{2})}((3*2x)ln(2) + \frac{(3x^{2})(0)}{(2)})){a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 8x^{3}{2}^{(3x^{2})}({a}^{(3 * {2}^{x^{2}})}((3({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{(3 * {2}^{x^{2}})(0)}{(a)}))e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 8x^{3}{2}^{(3x^{2})}{a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}({a}^{{2}^{x^{2}}}((({2}^{x^{2}}((2x)ln(2) + \frac{(x^{2})(0)}{(2)})))ln(a) + \frac{({2}^{x^{2}})(0)}{(a)}))ln^{3}(2)ln^{3}(a) + \frac{8x^{3}{2}^{(3x^{2})}{a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}*3ln^{2}(2)*0ln^{3}(a)}{(2)} + \frac{8x^{3}{2}^{(3x^{2})}{a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)*3ln^{2}(a)*0}{(a)}\\=&12 * {2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln(a) + 48x^{2}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln(a) + 144x^{2}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 144x^{2}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{2}(a) + 4 * {2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 48x^{2}{2}^{(3x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 144x^{2}{2}^{(3x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 4 * {2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(a)ln^{2}(2) + 48x^{2}{2}^{(3x^{2})}{a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{3}(2)ln^{3}(a) + 16x^{4}{2}^{x^{2}}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln(a) + 112x^{4}{2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln^{2}(a) + 112x^{4}{2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln^{2}(a) + 96x^{4}{2}^{(3x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln^{3}(a) + 288x^{4}{2}^{(3x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln^{3}(a) + 96x^{4}{2}^{(3x^{2})}{a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln^{3}(a) + 8 * {2}^{(2x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 16x^{4}{2}^{(4x^{2})}{a}^{{2}^{x^{2}}}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln^{4}(a) + 112x^{4}{2}^{(4x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln^{4}(a) + 96x^{4}{2}^{(4x^{2})}{a}^{(3 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln^{4}(a) + 8 * {2}^{(2x^{2})}{a}^{(2 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{2}(2)ln^{2}(a) + 16x^{4}{2}^{(4x^{2})}{a}^{(4 * {2}^{x^{2}})}e^{{a}^{{2}^{x^{2}}}}ln^{4}(2)ln^{4}(a)\\ \end{split}\end{equation} \]