There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{d({x}^{x})}{(dx)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{x}^{x}}{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{x}^{x}}{x}\right)}{dx}\\=&\frac{-{x}^{x}}{x^{2}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x}\\=&\frac{{x}^{x}ln(x)}{x} - \frac{{x}^{x}}{x^{2}} + \frac{{x}^{x}}{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{{x}^{x}ln(x)}{x} - \frac{{x}^{x}}{x^{2}} + \frac{{x}^{x}}{x}\right)}{dx}\\=&\frac{-{x}^{x}ln(x)}{x^{2}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x} + \frac{{x}^{x}}{x(x)} - \frac{-2{x}^{x}}{x^{3}} - \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}} + \frac{-{x}^{x}}{x^{2}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x}\\=&\frac{-2{x}^{x}ln(x)}{x^{2}} + \frac{{x}^{x}ln^{2}(x)}{x} + \frac{2{x}^{x}ln(x)}{x} + \frac{2{x}^{x}}{x^{3}} - \frac{{x}^{x}}{x^{2}} + \frac{{x}^{x}}{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( \frac{-2{x}^{x}ln(x)}{x^{2}} + \frac{{x}^{x}ln^{2}(x)}{x} + \frac{2{x}^{x}ln(x)}{x} + \frac{2{x}^{x}}{x^{3}} - \frac{{x}^{x}}{x^{2}} + \frac{{x}^{x}}{x}\right)}{dx}\\=&\frac{-2*-2{x}^{x}ln(x)}{x^{3}} - \frac{2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x^{2}} - \frac{2{x}^{x}}{x^{2}(x)} + \frac{-{x}^{x}ln^{2}(x)}{x^{2}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x} + \frac{{x}^{x}*2ln(x)}{x(x)} + \frac{2*-{x}^{x}ln(x)}{x^{2}} + \frac{2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x} + \frac{2{x}^{x}}{x(x)} + \frac{2*-3{x}^{x}}{x^{4}} + \frac{2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{3}} - \frac{-2{x}^{x}}{x^{3}} - \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{2}} + \frac{-{x}^{x}}{x^{2}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x}\\=&\frac{6{x}^{x}ln(x)}{x^{3}} - \frac{3{x}^{x}ln^{2}(x)}{x^{2}} + \frac{{x}^{x}ln^{3}(x)}{x} + \frac{3{x}^{x}ln^{2}(x)}{x} - \frac{3{x}^{x}ln(x)}{x^{2}} + \frac{3{x}^{x}ln(x)}{x} - \frac{6{x}^{x}}{x^{4}} + \frac{2{x}^{x}}{x^{3}} + \frac{{x}^{x}}{x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( \frac{6{x}^{x}ln(x)}{x^{3}} - \frac{3{x}^{x}ln^{2}(x)}{x^{2}} + \frac{{x}^{x}ln^{3}(x)}{x} + \frac{3{x}^{x}ln^{2}(x)}{x} - \frac{3{x}^{x}ln(x)}{x^{2}} + \frac{3{x}^{x}ln(x)}{x} - \frac{6{x}^{x}}{x^{4}} + \frac{2{x}^{x}}{x^{3}} + \frac{{x}^{x}}{x}\right)}{dx}\\=&\frac{6*-3{x}^{x}ln(x)}{x^{4}} + \frac{6({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x^{3}} + \frac{6{x}^{x}}{x^{3}(x)} - \frac{3*-2{x}^{x}ln^{2}(x)}{x^{3}} - \frac{3({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x^{2}} - \frac{3{x}^{x}*2ln(x)}{x^{2}(x)} + \frac{-{x}^{x}ln^{3}(x)}{x^{2}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{3}(x)}{x} + \frac{{x}^{x}*3ln^{2}(x)}{x(x)} + \frac{3*-{x}^{x}ln^{2}(x)}{x^{2}} + \frac{3({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x)}{x} + \frac{3{x}^{x}*2ln(x)}{x(x)} - \frac{3*-2{x}^{x}ln(x)}{x^{3}} - \frac{3({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x)}{x^{2}} - \frac{3{x}^{x}}{x^{2}(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)} - \frac{6*-4{x}^{x}}{x^{5}} - \frac{6({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{4}} + \frac{2*-3{x}^{x}}{x^{4}} + \frac{2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x^{3}} + \frac{-{x}^{x}}{x^{2}} + \frac{({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x}\\=&\frac{-24{x}^{x}ln(x)}{x^{4}} + \frac{12{x}^{x}ln^{2}(x)}{x^{3}} - \frac{4{x}^{x}ln^{3}(x)}{x^{2}} + \frac{{x}^{x}ln^{4}(x)}{x} + \frac{4{x}^{x}ln^{3}(x)}{x} - \frac{6{x}^{x}ln^{2}(x)}{x^{2}} + \frac{6{x}^{x}ln^{2}(x)}{x} + \frac{8{x}^{x}ln(x)}{x^{3}} + \frac{4{x}^{x}ln(x)}{x} - \frac{{x}^{x}}{x^{3}} + \frac{2{x}^{x}}{x^{2}} + \frac{24{x}^{x}}{x^{5}} - \frac{6{x}^{x}}{x^{4}} + \frac{{x}^{x}}{x}\\ \end{split}\end{equation} \]

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