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

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