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

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