There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ tan(1 + {(tan(2x))}^{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = tan(tan^{2}(2x) + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( tan(tan^{2}(2x) + 1)\right)}{dx}\\=&sec^{2}(tan^{2}(2x) + 1)(2tan(2x)sec^{2}(2x)(2) + 0)\\=&4tan(2x)sec^{2}(2x)sec^{2}(tan^{2}(2x) + 1)\\ \end{split}\end{equation} \]

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