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

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