There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{2ln(1 + 2tan(x))}{5} - \frac{ln(1 + (tan(x))(tan(x)))}{5} + \frac{x}{5}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{2}{5}ln(2tan(x) + 1) - \frac{1}{5}ln(tan^{2}(x) + 1) + \frac{1}{5}x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{2}{5}ln(2tan(x) + 1) - \frac{1}{5}ln(tan^{2}(x) + 1) + \frac{1}{5}x\right)}{dx}\\=&\frac{\frac{2}{5}(2sec^{2}(x)(1) + 0)}{(2tan(x) + 1)} - \frac{\frac{1}{5}(2tan(x)sec^{2}(x)(1) + 0)}{(tan^{2}(x) + 1)} + \frac{1}{5}\\=&\frac{4sec^{2}(x)}{5(2tan(x) + 1)} - \frac{2tan(x)sec^{2}(x)}{5(tan^{2}(x) + 1)} + \frac{1}{5}\\ \end{split}\end{equation} \]

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