There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (x - ln(1 + x)){\frac{1}{(tan(x))}}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x}{tan^{2}(x)} - \frac{ln(x + 1)}{tan^{2}(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x}{tan^{2}(x)} - \frac{ln(x + 1)}{tan^{2}(x)}\right)}{dx}\\=&\frac{1}{tan^{2}(x)} + \frac{x*-2sec^{2}(x)(1)}{tan^{3}(x)} - \frac{(1 + 0)}{(x + 1)tan^{2}(x)} - \frac{ln(x + 1)*-2sec^{2}(x)(1)}{tan^{3}(x)}\\=&\frac{1}{tan^{2}(x)} - \frac{2xsec^{2}(x)}{tan^{3}(x)} - \frac{1}{(x + 1)tan^{2}(x)} + \frac{2ln(x + 1)sec^{2}(x)}{tan^{3}(x)}\\ \end{split}\end{equation} \]

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