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

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