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

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