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

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