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

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