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

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