There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (2{x}^{2}y + 2y){y}^{(2{x}^{2} + 1)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 2yx^{2}{y}^{(2x^{2} + 1)} + 2y{y}^{(2x^{2} + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 2yx^{2}{y}^{(2x^{2} + 1)} + 2y{y}^{(2x^{2} + 1)}\right)}{dx}\\=&2y*2x{y}^{(2x^{2} + 1)} + 2yx^{2}({y}^{(2x^{2} + 1)}((2*2x + 0)ln(y) + \frac{(2x^{2} + 1)(0)}{(y)})) + 2y({y}^{(2x^{2} + 1)}((2*2x + 0)ln(y) + \frac{(2x^{2} + 1)(0)}{(y)}))\\=&8yx^{3}{y}^{(2x^{2} + 1)}ln(y) + 8yx{y}^{(2x^{2} + 1)}ln(y) + 4yx{y}^{(2x^{2} + 1)}\\ \end{split}\end{equation} \]

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