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

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