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

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