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.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {x}^{{4}^{(1 + {x}^{3})}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {x}^{{4}^{(x^{3} + 1)}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {x}^{{4}^{(x^{3} + 1)}}\right)}{dx}\\=&({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))\\=&3x^{2}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + \frac{{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3x^{2}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + \frac{{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x}\right)}{dx}\\=&3*2x{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 3x^{2}({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 3x^{2}{4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln(x)ln(4) + \frac{3x^{2}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(4)}{(x)} + \frac{3x^{2}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)*0}{(4)} + \frac{-{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x^{2}} + \frac{({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}}{x} + \frac{{4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))}{x}\\=&6x{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 9x^{4}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 9x^{4}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{2}(4) + 6x{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 3x{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln(4) + 3x{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(4) - \frac{{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x^{2}} + \frac{{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}}{x^{2}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 6x{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 9x^{4}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 9x^{4}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{2}(4) + 6x{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 3x{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln(4) + 3x{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(4) - \frac{{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x^{2}} + \frac{{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}}{x^{2}}\right)}{dx}\\=&6 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 6x({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 6x{4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln(x)ln(4) + \frac{6x{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(4)}{(x)} + \frac{6x{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)*0}{(4)} + 9*4x^{3}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 9x^{4}({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 9x^{4}{4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{2}(4)ln(x) + \frac{9x^{4}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}*2ln(4)*0ln(x)}{(4)} + \frac{9x^{4}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)}{(x)} + 9*4x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{2}(4) + 9x^{4}({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{2}(4) + 9x^{4}{4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{2}(x)ln^{2}(4) + \frac{9x^{4}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}*2ln(x)ln^{2}(4)}{(x)} + \frac{9x^{4}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)*2ln(4)*0}{(4)} + 6 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 6x({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 6x{4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln(x)ln(4) + \frac{6x{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(4)}{(x)} + \frac{6x{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)*0}{(4)} + 3{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln(4) + 3x({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)})){4}^{(x^{3} + 1)}ln(4) + 3x{x}^{{4}^{(x^{3} + 1)}}({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)}))ln(4) + \frac{3x{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}*0}{(4)} + 3 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(4) + 3x({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln(4) + 3x{4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln(4) + \frac{3x{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}*0}{(4)} - \frac{-2 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x^{3}} - \frac{({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}}{x^{2}} - \frac{{4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))}{x^{2}} + \frac{-2 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}}{x^{3}} + \frac{({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}}{x^{2}} + \frac{{4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))}{x^{2}}\\=&6 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 54x^{3}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 81x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{2}(4) + 18 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 27x^{6}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln(x) + 27x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{3}(4) + 45x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 36x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln^{2}(4) + 54x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln^{2}(x) + 27x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(x)ln^{3}(4) + 9{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln(4) + 6{x}^{{4}^{(x^{3} + 1)}}{4}^{(2x^{3} + 2)}ln(4) + 9x^{3}{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln^{2}(4) + 12 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(4) + 18x^{3}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4) + \frac{2 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x^{3}} - \frac{2 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}}{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 6 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 54x^{3}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 81x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{2}(4) + 18 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 27x^{6}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln(x) + 27x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{3}(4) + 45x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 36x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln^{2}(4) + 54x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln^{2}(x) + 27x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(x)ln^{3}(4) + 9{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln(4) + 6{x}^{{4}^{(x^{3} + 1)}}{4}^{(2x^{3} + 2)}ln(4) + 9x^{3}{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln^{2}(4) + 12 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(4) + 18x^{3}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4) + \frac{2 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x^{3}} - \frac{2 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}}{x^{3}}\right)}{dx}\\=&6({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 6 * {4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln(x)ln(4) + \frac{6 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(4)}{(x)} + \frac{6 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(x)*0}{(4)} + 54*3x^{2}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 54x^{3}({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 54x^{3}{4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{2}(4)ln(x) + \frac{54x^{3}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}*2ln(4)*0ln(x)}{(4)} + \frac{54x^{3}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)}{(x)} + 81*3x^{2}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{2}(4) + 81x^{3}({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{2}(4) + 81x^{3}{4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{2}(x)ln^{2}(4) + \frac{81x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}*2ln(x)ln^{2}(4)}{(x)} + \frac{81x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)*2ln(4)*0}{(4)} + 18({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4) + 18 * {4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln(x)ln(4) + \frac{18 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(4)}{(x)} + \frac{18 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)*0}{(4)} + 27*6x^{5}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln(x) + 27x^{6}({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln(x) + 27x^{6}{4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{3}(4)ln(x) + \frac{27x^{6}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}*3ln^{2}(4)*0ln(x)}{(4)} + \frac{27x^{6}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)}{(x)} + 27*6x^{5}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{3}(4) + 27x^{6}({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{3}(4) + 27x^{6}{4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{2}(x)ln^{3}(4) + \frac{27x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}*2ln(x)ln^{3}(4)}{(x)} + \frac{27x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)*3ln^{2}(4)*0}{(4)} + 45*3x^{2}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 45x^{3}({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 45x^{3}{4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{2}(4)ln(x) + \frac{45x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}*2ln(4)*0ln(x)}{(4)} + \frac{45x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)}{(x)} + 36*3x^{2}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln^{2}(4) + 36x^{3}({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln(x)ln^{2}(4) + 36x^{3}{4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln(x)ln^{2}(4) + \frac{36x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)}{(x)} + \frac{36x^{3}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)*2ln(4)*0}{(4)} + 54*6x^{5}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln^{2}(x) + 54x^{6}({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln^{2}(x) + 54x^{6}{4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{3}(4)ln^{2}(x) + \frac{54x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}*3ln^{2}(4)*0ln^{2}(x)}{(4)} + \frac{54x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)*2ln(x)}{(x)} + 27*6x^{5}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(x)ln^{3}(4) + 27x^{6}({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{3}(x)ln^{3}(4) + 27x^{6}{4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{3}(x)ln^{3}(4) + \frac{27x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}*3ln^{2}(x)ln^{3}(4)}{(x)} + \frac{27x^{6}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(x)*3ln^{2}(4)*0}{(4)} + 9({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)})){4}^{(x^{3} + 1)}ln(4) + 9{x}^{{4}^{(x^{3} + 1)}}({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)}))ln(4) + \frac{9{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}*0}{(4)} + 6({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)})){4}^{(2x^{3} + 2)}ln(4) + 6{x}^{{4}^{(x^{3} + 1)}}({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)}))ln(4) + \frac{6{x}^{{4}^{(x^{3} + 1)}}{4}^{(2x^{3} + 2)}*0}{(4)} + 9*3x^{2}{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln^{2}(4) + 9x^{3}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)})){4}^{(x^{3} + 1)}ln^{2}(4) + 9x^{3}{x}^{{4}^{(x^{3} + 1)}}({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)}))ln^{2}(4) + \frac{9x^{3}{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}*2ln(4)*0}{(4)} + 12({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln(4) + 12 * {4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln(4) + \frac{12 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}*0}{(4)} + 18*3x^{2}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4) + 18x^{3}({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}ln^{2}(4) + 18x^{3}{4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))ln^{2}(4) + \frac{18x^{3}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}*2ln(4)*0}{(4)} + \frac{2*-3 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x^{4}} + \frac{2({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}}{x^{3}} + \frac{2 * {4}^{(x^{3} + 1)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))}{x^{3}} - \frac{2*-3 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}}{x^{4}} - \frac{2({4}^{(2x^{3} + 2)}((2*3x^{2} + 0)ln(4) + \frac{(2x^{3} + 2)(0)}{(4)})){x}^{{4}^{(x^{3} + 1)}}}{x^{3}} - \frac{2 * {4}^{(2x^{3} + 2)}({x}^{{4}^{(x^{3} + 1)}}((({4}^{(x^{3} + 1)}((3x^{2} + 0)ln(4) + \frac{(x^{3} + 1)(0)}{(4)})))ln(x) + \frac{({4}^{(x^{3} + 1)})(1)}{(x)}))}{x^{3}}\\=&180x^{2}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 72x^{2}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln^{2}(x) + \frac{24 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln(4)}{x} + 324x^{2}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{2}(4) + 324x^{5}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln(x) + 675x^{5}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{3}(4) + 423x^{2}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4)ln(x) + 306x^{2}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln^{2}(4) + 864x^{5}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln^{2}(x) + 432x^{5}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(x)ln^{3}(4) + 243x^{5}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(x)ln^{3}(4) + 81x^{8}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{4}(4)ln(x) + 81x^{8}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(x)ln^{4}(4) + 513x^{5}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4)ln(x) + 486x^{8}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{4}(4)ln^{2}(x) + 243x^{8}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(x)ln^{4}(4) + 162x^{8}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{4}(4)ln^{3}(x) + 81x^{8}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{4}(x)ln^{4}(4) + \frac{6{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln(4)}{x} + 81x^{2}{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln^{2}(4) + 81x^{2}{x}^{{4}^{(x^{3} + 1)}}{4}^{(2x^{3} + 2)}ln^{2}(4) + \frac{18{x}^{{4}^{(x^{3} + 1)}}{4}^{(2x^{3} + 2)}ln(4)}{x} + \frac{15 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln(4)}{x} + 81x^{2}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4) + 135x^{2}{4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}ln^{2}(4) + 27x^{5}{x}^{{4}^{(x^{3} + 1)}}{4}^{(x^{3} + 1)}ln^{3}(4) + 81x^{5}{4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln^{3}(4) + \frac{6 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}ln(4)}{x} + \frac{6 * {4}^{(2x^{3} + 2)}{x}^{{4}^{(x^{3} + 1)}}}{x^{4}} - \frac{6 * {4}^{(x^{3} + 1)}{x}^{{4}^{(x^{3} + 1)}}}{x^{4}}\\ \end{split}\end{equation} \]