There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {e}^{{x}^{3}}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = {e}^{x^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e}^{x^{3}}\right)}{dx}\\=&({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)}))\\=&3x^{2}{e}^{x^{3}}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 3x^{2}{e}^{x^{3}}\right)}{dx}\\=&3*2x{e}^{x^{3}} + 3x^{2}({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)}))\\=&6x{e}^{x^{3}} + 9x^{4}{e}^{x^{3}}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 6x{e}^{x^{3}} + 9x^{4}{e}^{x^{3}}\right)}{dx}\\=&6{e}^{x^{3}} + 6x({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)})) + 9*4x^{3}{e}^{x^{3}} + 9x^{4}({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)}))\\=&6{e}^{x^{3}} + 54x^{3}{e}^{x^{3}} + 27x^{6}{e}^{x^{3}}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 6{e}^{x^{3}} + 54x^{3}{e}^{x^{3}} + 27x^{6}{e}^{x^{3}}\right)}{dx}\\=&6({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)})) + 54*3x^{2}{e}^{x^{3}} + 54x^{3}({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)})) + 27*6x^{5}{e}^{x^{3}} + 27x^{6}({e}^{x^{3}}((3x^{2})ln(e) + \frac{(x^{3})(0)}{(e)}))\\=&180x^{2}{e}^{x^{3}} + 324x^{5}{e}^{x^{3}} + 81x^{8}{e}^{x^{3}}\\ \end{split}\end{equation} \]

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