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

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