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

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