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

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