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

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