There are 1 questions in this calculation: for each question, the 2 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ second\ derivative\ of\ function\ \frac{(tan(x))}{(tan(3x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{tan(x)}{tan(3x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{tan(x)}{tan(3x)}\right)}{dx}\\=&\frac{sec^{2}(x)(1)}{tan(3x)} + \frac{tan(x)*-sec^{2}(3x)(3)}{tan^{2}(3x)}\\=&\frac{sec^{2}(x)}{tan(3x)} - \frac{3tan(x)sec^{2}(3x)}{tan^{2}(3x)}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( \frac{sec^{2}(x)}{tan(3x)} - \frac{3tan(x)sec^{2}(3x)}{tan^{2}(3x)}\right)}{dx}\\=&\frac{-sec^{2}(3x)(3)sec^{2}(x)}{tan^{2}(3x)} + \frac{2sec^{2}(x)tan(x)}{tan(3x)} - \frac{3*-2sec^{2}(3x)(3)tan(x)sec^{2}(3x)}{tan^{3}(3x)} - \frac{3sec^{2}(x)(1)sec^{2}(3x)}{tan^{2}(3x)} - \frac{3tan(x)*2sec^{2}(3x)tan(3x)*3}{tan^{2}(3x)}\\=&\frac{-3sec^{2}(3x)sec^{2}(x)}{tan^{2}(3x)} + \frac{18tan(x)sec^{4}(3x)}{tan^{3}(3x)} + \frac{2tan(x)sec^{2}(x)}{tan(3x)} - \frac{3sec^{2}(x)sec^{2}(3x)}{tan^{2}(3x)} - \frac{18tan(x)sec^{2}(3x)}{tan(3x)}\\ \end{split}\end{equation} \]

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