There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (ln(1 + {\frac{1}{100}}^{x})) - {(1 + {100}^{x})}^{\frac{1}{x}} + 100\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln({\frac{1}{100}}^{x} + 1) - ({100}^{x} + 1)^{\frac{1}{x}} + 100\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln({\frac{1}{100}}^{x} + 1) - ({100}^{x} + 1)^{\frac{1}{x}} + 100\right)}{dx}\\=&\frac{(({\frac{1}{100}}^{x}((1)ln(\frac{1}{100}) + \frac{(x)(0)}{(\frac{1}{100})})) + 0)}{({\frac{1}{100}}^{x} + 1)} - (({100}^{x} + 1)^{\frac{1}{x}}((\frac{-1}{x^{2}})ln({100}^{x} + 1) + \frac{(\frac{1}{x})(({100}^{x}((1)ln(100) + \frac{(x)(0)}{(100)})) + 0)}{({100}^{x} + 1)})) + 0\\=&\frac{{\frac{1}{100}}^{x}ln(\frac{1}{100})}{({\frac{1}{100}}^{x} + 1)} + \frac{({100}^{x} + 1)^{\frac{1}{x}}ln({100}^{x} + 1)}{x^{2}} - \frac{{100}^{x}({100}^{x} + 1)^{\frac{1}{x}}ln(100)}{({100}^{x} + 1)x}\\ \end{split}\end{equation} \]

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