There are 1 questions in this calculation: for each question, the 5 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 5th\ derivative\ of\ function\ sin({x}^{x})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ \\ &\color{blue}{The\ 5th\ derivative\ of\ function:} \\=&{x}^{x}ln^{5}(x)cos({x}^{x}) + 5{x}^{x}ln^{4}(x)cos({x}^{x}) + \frac{10{x}^{x}ln^{3}(x)cos({x}^{x})}{x} - 15{x}^{(2x)}ln^{5}(x)sin({x}^{x}) - 75{x}^{(2x)}ln^{4}(x)sin({x}^{x}) + 10{x}^{x}ln^{3}(x)cos({x}^{x}) + \frac{30{x}^{x}ln^{2}(x)cos({x}^{x})}{x} - 150{x}^{(2x)}ln^{3}(x)sin({x}^{x}) - \frac{10{x}^{x}ln^{2}(x)cos({x}^{x})}{x^{2}} - \frac{70{x}^{(2x)}ln^{3}(x)sin({x}^{x})}{x} - \frac{210{x}^{(2x)}ln^{2}(x)sin({x}^{x})}{x} - 25{x}^{(3x)}ln^{5}(x)cos({x}^{x}) - 125{x}^{(3x)}ln^{4}(x)cos({x}^{x}) - 250{x}^{(3x)}ln^{3}(x)cos({x}^{x}) + 10{x}^{x}ln^{2}(x)cos({x}^{x}) + \frac{30{x}^{x}ln(x)cos({x}^{x})}{x} - 150{x}^{(2x)}ln^{2}(x)sin({x}^{x}) + \frac{5{x}^{x}cos({x}^{x})}{x^{2}} - \frac{210{x}^{(2x)}ln(x)sin({x}^{x})}{x} - 250{x}^{(3x)}ln^{2}(x)cos({x}^{x}) + \frac{10{x}^{x}ln(x)cos({x}^{x})}{x^{3}} - \frac{5{x}^{x}ln(x)cos({x}^{x})}{x^{2}} + \frac{30{x}^{(2x)}ln^{2}(x)sin({x}^{x})}{x^{2}} + \frac{15{x}^{(2x)}ln(x)sin({x}^{x})}{x^{2}} - \frac{60{x}^{(3x)}ln^{3}(x)cos({x}^{x})}{x} - \frac{180{x}^{(3x)}ln^{2}(x)cos({x}^{x})}{x} - \frac{15{x}^{(2x)}sin({x}^{x})}{x^{2}} - \frac{180{x}^{(3x)}ln(x)cos({x}^{x})}{x} + 10{x}^{(4x)}ln^{5}(x)sin({x}^{x}) + 50{x}^{(4x)}ln^{4}(x)sin({x}^{x}) + 100{x}^{(4x)}ln^{3}(x)sin({x}^{x}) + 100{x}^{(4x)}ln^{2}(x)sin({x}^{x}) + 5{x}^{x}ln(x)cos({x}^{x}) + \frac{10{x}^{x}cos({x}^{x})}{x} - 75{x}^{(2x)}ln(x)sin({x}^{x}) - \frac{70{x}^{(2x)}sin({x}^{x})}{x} - 125{x}^{(3x)}ln(x)cos({x}^{x}) - \frac{60{x}^{(3x)}cos({x}^{x})}{x} + 50{x}^{(4x)}ln(x)sin({x}^{x}) - \frac{6{x}^{x}cos({x}^{x})}{x^{4}} - \frac{10{x}^{(2x)}ln(x)sin({x}^{x})}{x^{3}} + \frac{10{x}^{(3x)}ln^{2}(x)cos({x}^{x})}{x^{2}} + \frac{5{x}^{(3x)}ln(x)cos({x}^{x})}{x^{2}} - \frac{5{x}^{(3x)}cos({x}^{x})}{x^{2}} + \frac{10{x}^{(4x)}ln^{3}(x)sin({x}^{x})}{x} + \frac{30{x}^{(4x)}ln^{2}(x)sin({x}^{x})}{x} + \frac{30{x}^{(4x)}ln(x)sin({x}^{x})}{x} + \frac{10{x}^{(4x)}sin({x}^{x})}{x} + {x}^{(5x)}ln^{5}(x)cos({x}^{x}) + 5{x}^{(5x)}ln^{4}(x)cos({x}^{x}) + 10{x}^{(5x)}ln^{3}(x)cos({x}^{x}) + 10{x}^{(5x)}ln^{2}(x)cos({x}^{x}) + 5{x}^{(5x)}ln(x)cos({x}^{x}) + {x}^{x}cos({x}^{x}) - 15{x}^{(2x)}sin({x}^{x}) - 25{x}^{(3x)}cos({x}^{x}) + 10{x}^{(4x)}sin({x}^{x}) + {x}^{(5x)}cos({x}^{x})\\ \end{split}\end{equation} \]

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