There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(sin(x)x)}{({(1 + {e}^{x})}^{3}(cos(x)))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{xsin(x)}{({e}^{x} + 1)^{3}cos(x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{xsin(x)}{({e}^{x} + 1)^{3}cos(x)}\right)}{dx}\\=&\frac{(\frac{-3(({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 0)}{({e}^{x} + 1)^{4}})xsin(x)}{cos(x)} + \frac{sin(x)}{({e}^{x} + 1)^{3}cos(x)} + \frac{xcos(x)}{({e}^{x} + 1)^{3}cos(x)} + \frac{xsin(x)sin(x)}{({e}^{x} + 1)^{3}cos^{2}(x)}\\=&\frac{-3x{e}^{x}sin(x)}{({e}^{x} + 1)^{4}cos(x)} + \frac{sin(x)}{({e}^{x} + 1)^{3}cos(x)} + \frac{xsin^{2}(x)}{({e}^{x} + 1)^{3}cos^{2}(x)} + \frac{x}{({e}^{x} + 1)^{3}}\\ \end{split}\end{equation} \]

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