There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(4{x}^{2} + 4x + 1)}{(x + {sin(x)}^{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{4x^{2}}{(x + sin^{2}(x))} + \frac{4x}{(x + sin^{2}(x))} + \frac{1}{(x + sin^{2}(x))}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{4x^{2}}{(x + sin^{2}(x))} + \frac{4x}{(x + sin^{2}(x))} + \frac{1}{(x + sin^{2}(x))}\right)}{dx}\\=&4(\frac{-(1 + 2sin(x)cos(x))}{(x + sin^{2}(x))^{2}})x^{2} + \frac{4*2x}{(x + sin^{2}(x))} + 4(\frac{-(1 + 2sin(x)cos(x))}{(x + sin^{2}(x))^{2}})x + \frac{4}{(x + sin^{2}(x))} + (\frac{-(1 + 2sin(x)cos(x))}{(x + sin^{2}(x))^{2}})\\=&\frac{-8x^{2}sin(x)cos(x)}{(x + sin^{2}(x))^{2}} - \frac{8xsin(x)cos(x)}{(x + sin^{2}(x))^{2}} + \frac{8x}{(x + sin^{2}(x))} - \frac{4x^{2}}{(x + sin^{2}(x))^{2}} - \frac{4x}{(x + sin^{2}(x))^{2}} - \frac{2sin(x)cos(x)}{(x + sin^{2}(x))^{2}} + \frac{4}{(x + sin^{2}(x))} - \frac{1}{(x + sin^{2}(x))^{2}}\\ \end{split}\end{equation} \]

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