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

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