There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{cot(sqrt({x}^{2} + sin(x)))log*7*3x}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{21}{2}logxcot(sqrt(x^{2} + sin(x)))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{21}{2}logxcot(sqrt(x^{2} + sin(x)))\right)}{dx}\\=&\frac{21}{2}logcot(sqrt(x^{2} + sin(x))) + \frac{\frac{21}{2}logx*-csc^{2}(sqrt(x^{2} + sin(x)))(2x + cos(x))*\frac{1}{2}}{(x^{2} + sin(x))^{\frac{1}{2}}}\\=&\frac{21logcot(sqrt(x^{2} + sin(x)))}{2} - \frac{21logx^{2}csc^{2}(sqrt(x^{2} + sin(x)))}{2(x^{2} + sin(x))^{\frac{1}{2}}} - \frac{21logxcos(x)csc^{2}(sqrt(x^{2} + sin(x)))}{4(x^{2} + sin(x))^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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