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

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