There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ {e^{x}}^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( {e^{x}}^{x}\right)}{dx}\\=&({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))\\=&{e^{x}}^{x}ln(e^{x}) + x{e^{x}}^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {e^{x}}^{x}ln(e^{x}) + x{e^{x}}^{x}\right)}{dx}\\=&({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))ln(e^{x}) + \frac{{e^{x}}^{x}e^{x}}{(e^{x})} + {e^{x}}^{x} + x({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))\\=&{e^{x}}^{x}ln^{2}(e^{x}) + 2x{e^{x}}^{x}ln(e^{x}) + 2{e^{x}}^{x} + x^{2}{e^{x}}^{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( {e^{x}}^{x}ln^{2}(e^{x}) + 2x{e^{x}}^{x}ln(e^{x}) + 2{e^{x}}^{x} + x^{2}{e^{x}}^{x}\right)}{dx}\\=&({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))ln^{2}(e^{x}) + \frac{{e^{x}}^{x}*2ln(e^{x})e^{x}}{(e^{x})} + 2{e^{x}}^{x}ln(e^{x}) + 2x({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))ln(e^{x}) + \frac{2x{e^{x}}^{x}e^{x}}{(e^{x})} + 2({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})})) + 2x{e^{x}}^{x} + x^{2}({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))\\=&{e^{x}}^{x}ln^{3}(e^{x}) + 3x{e^{x}}^{x}ln^{2}(e^{x}) + 6{e^{x}}^{x}ln(e^{x}) + 3x^{2}{e^{x}}^{x}ln(e^{x}) + 6x{e^{x}}^{x} + x^{3}{e^{x}}^{x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( {e^{x}}^{x}ln^{3}(e^{x}) + 3x{e^{x}}^{x}ln^{2}(e^{x}) + 6{e^{x}}^{x}ln(e^{x}) + 3x^{2}{e^{x}}^{x}ln(e^{x}) + 6x{e^{x}}^{x} + x^{3}{e^{x}}^{x}\right)}{dx}\\=&({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))ln^{3}(e^{x}) + \frac{{e^{x}}^{x}*3ln^{2}(e^{x})e^{x}}{(e^{x})} + 3{e^{x}}^{x}ln^{2}(e^{x}) + 3x({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))ln^{2}(e^{x}) + \frac{3x{e^{x}}^{x}*2ln(e^{x})e^{x}}{(e^{x})} + 6({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))ln(e^{x}) + \frac{6{e^{x}}^{x}e^{x}}{(e^{x})} + 3*2x{e^{x}}^{x}ln(e^{x}) + 3x^{2}({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))ln(e^{x}) + \frac{3x^{2}{e^{x}}^{x}e^{x}}{(e^{x})} + 6{e^{x}}^{x} + 6x({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})})) + 3x^{2}{e^{x}}^{x} + x^{3}({e^{x}}^{x}((1)ln(e^{x}) + \frac{(x)(e^{x})}{(e^{x})}))\\=&{e^{x}}^{x}ln^{4}(e^{x}) + 4x{e^{x}}^{x}ln^{3}(e^{x}) + 12{e^{x}}^{x}ln^{2}(e^{x}) + 6x^{2}{e^{x}}^{x}ln^{2}(e^{x}) + 24x{e^{x}}^{x}ln(e^{x}) + 12{e^{x}}^{x} + 4x^{3}{e^{x}}^{x}ln(e^{x}) + 12x^{2}{e^{x}}^{x} + x^{4}{e^{x}}^{x}\\ \end{split}\end{equation} \]

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