There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{cot(sqrt({x}^{2} + sin(x)))log_{7}^{3x}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}log_{7}^{3x}cot(sqrt(x^{2} + sin(x)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}log_{7}^{3x}cot(sqrt(x^{2} + sin(x)))\right)}{dx}\\=&\frac{1}{2}(\frac{(\frac{(3)}{(3x)} - \frac{(0)log_{7}^{3x}}{(7)})}{(ln(7))})cot(sqrt(x^{2} + sin(x))) + \frac{\frac{1}{2}log_{7}^{3x}*-csc^{2}(sqrt(x^{2} + sin(x)))(2x + cos(x))*\frac{1}{2}}{(x^{2} + sin(x))^{\frac{1}{2}}}\\=&\frac{cot(sqrt(x^{2} + sin(x)))}{2xln(7)} - \frac{xlog_{7}^{3x}csc^{2}(sqrt(x^{2} + sin(x)))}{2(x^{2} + sin(x))^{\frac{1}{2}}} - \frac{log_{7}^{3x}cos(x)csc^{2}(sqrt(x^{2} + sin(x)))}{4(x^{2} + sin(x))^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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