There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ({({x}^{2} + sin(2x))}^{x}){(x - 1)}^{(\frac{2}{5})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x - 1)^{\frac{2}{5}}(x^{2} + sin(2x))^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x - 1)^{\frac{2}{5}}(x^{2} + sin(2x))^{x}\right)}{dx}\\=&(\frac{\frac{2}{5}(1 + 0)}{(x - 1)^{\frac{3}{5}}})(x^{2} + sin(2x))^{x} + (x - 1)^{\frac{2}{5}}((x^{2} + sin(2x))^{x}((1)ln(x^{2} + sin(2x)) + \frac{(x)(2x + cos(2x)*2)}{(x^{2} + sin(2x))}))\\=&(x - 1)^{\frac{2}{5}}(x^{2} + sin(2x))^{x}ln(x^{2} + sin(2x)) + \frac{2(x^{2} + sin(2x))^{x}}{5(x - 1)^{\frac{3}{5}}} + \frac{2(x - 1)^{\frac{2}{5}}x(x^{2} + sin(2x))^{x}cos(2x)}{(x^{2} + sin(2x))} + \frac{2(x - 1)^{\frac{2}{5}}x^{2}(x^{2} + sin(2x))^{x}}{(x^{2} + sin(2x))}\\ \end{split}\end{equation} \]

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