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

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