There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({(ln(x))}^{(3 + cos(x))} + (tan(x))(7x))}{(sin(x) + lg(x))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{{ln(x)}^{(cos(x) + 3)}}{(sin(x) + lg(x))} + \frac{7xtan(x)}{(sin(x) + lg(x))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{{ln(x)}^{(cos(x) + 3)}}{(sin(x) + lg(x))} + \frac{7xtan(x)}{(sin(x) + lg(x))}\right)}{dx}\\=&(\frac{-(cos(x) + \frac{1}{ln{10}(x)})}{(sin(x) + lg(x))^{2}}){ln(x)}^{(cos(x) + 3)} + \frac{({ln(x)}^{(cos(x) + 3)}((-sin(x) + 0)ln(ln(x)) + \frac{(cos(x) + 3)(\frac{1}{(x)})}{(ln(x))}))}{(sin(x) + lg(x))} + 7(\frac{-(cos(x) + \frac{1}{ln{10}(x)})}{(sin(x) + lg(x))^{2}})xtan(x) + \frac{7tan(x)}{(sin(x) + lg(x))} + \frac{7xsec^{2}(x)(1)}{(sin(x) + lg(x))}\\=&\frac{-{ln(x)}^{(cos(x) + 3)}cos(x)}{(sin(x) + lg(x))^{2}} + \frac{{ln(x)}^{(cos(x) + 3)}cos(x)}{(sin(x) + lg(x))xln(x)} - \frac{{ln(x)}^{(cos(x) + 3)}ln(ln(x))sin(x)}{(sin(x) + lg(x))} - \frac{{ln(x)}^{(cos(x) + 3)}}{(sin(x) + lg(x))^{2}xln{10}} + \frac{3{ln(x)}^{(cos(x) + 3)}}{(sin(x) + lg(x))xln(x)} - \frac{7xcos(x)tan(x)}{(sin(x) + lg(x))^{2}} - \frac{7tan(x)}{(sin(x) + lg(x))^{2}ln{10}} + \frac{7tan(x)}{(sin(x) + lg(x))} + \frac{7xsec^{2}(x)}{(sin(x) + lg(x))}\\ \end{split}\end{equation} \]

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