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

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