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

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