There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{1}{2}arctan(tan(x)tan(x))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}arctan(tan^{2}(x))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}arctan(tan^{2}(x))\right)}{dx}\\=&\frac{1}{2}(\frac{(2tan(x)sec^{2}(x)(1))}{(1 + (tan^{2}(x))^{2})})\\=&\frac{tan(x)sec^{2}(x)}{(tan^{4}(x) + 1)}\\ \end{split}\end{equation} \]

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