There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ \frac{d({x}^{x})x}{d}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x{x}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x{x}^{x}\right)}{dx}\\=&{x}^{x} + x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))\\=&{x}^{x} + x{x}^{x}ln(x) + x{x}^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( {x}^{x} + x{x}^{x}ln(x) + x{x}^{x}\right)}{dx}\\=&({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})) + {x}^{x}ln(x) + x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x) + \frac{x{x}^{x}}{(x)} + {x}^{x} + x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))\\=&2{x}^{x}ln(x) + 3{x}^{x} + x{x}^{x}ln^{2}(x) + 2x{x}^{x}ln(x) + x{x}^{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 2{x}^{x}ln(x) + 3{x}^{x} + x{x}^{x}ln^{2}(x) + 2x{x}^{x}ln(x) + x{x}^{x}\right)}{dx}\\=&2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x) + \frac{2{x}^{x}}{(x)} + 3({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})) + {x}^{x}ln^{2}(x) + x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x) + \frac{x{x}^{x}*2ln(x)}{(x)} + 2{x}^{x}ln(x) + 2x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x) + \frac{2x{x}^{x}}{(x)} + {x}^{x} + x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))\\=&3{x}^{x}ln^{2}(x) + 9{x}^{x}ln(x) + x{x}^{x}ln^{3}(x) + 6{x}^{x} + 3x{x}^{x}ln^{2}(x) + 3x{x}^{x}ln(x) + \frac{2{x}^{x}}{x} + x{x}^{x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 3{x}^{x}ln^{2}(x) + 9{x}^{x}ln(x) + x{x}^{x}ln^{3}(x) + 6{x}^{x} + 3x{x}^{x}ln^{2}(x) + 3x{x}^{x}ln(x) + \frac{2{x}^{x}}{x} + x{x}^{x}\right)}{dx}\\=&3({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x) + \frac{3{x}^{x}*2ln(x)}{(x)} + 9({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x) + \frac{9{x}^{x}}{(x)} + {x}^{x}ln^{3}(x) + x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{3}(x) + \frac{x{x}^{x}*3ln^{2}(x)}{(x)} + 6({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})) + 3{x}^{x}ln^{2}(x) + 3x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln^{2}(x) + \frac{3x{x}^{x}*2ln(x)}{(x)} + 3{x}^{x}ln(x) + 3x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))ln(x) + \frac{3x{x}^{x}}{(x)} + \frac{2*-{x}^{x}}{x^{2}} + \frac{2({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))}{x} + {x}^{x} + x({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)}))\\=&4{x}^{x}ln^{3}(x) + 18{x}^{x}ln^{2}(x) + \frac{8{x}^{x}ln(x)}{x} + 24{x}^{x}ln(x) + x{x}^{x}ln^{4}(x) + 4x{x}^{x}ln^{3}(x) + 6x{x}^{x}ln^{2}(x) + 10{x}^{x} + 4x{x}^{x}ln(x) + \frac{11{x}^{x}}{x} - \frac{2{x}^{x}}{x^{2}} + x{x}^{x}\\ \end{split}\end{equation} \]

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