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

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