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

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