There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sec(x{\frac{1}{5}}^{x}){(cos(x{\frac{1}{5}}^{x}))}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = cos^{2}(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x})\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( cos^{2}(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x})\right)}{dx}\\=&-2cos(x{\frac{1}{5}}^{x})sin(x{\frac{1}{5}}^{x})({\frac{1}{5}}^{x} + x({\frac{1}{5}}^{x}((1)ln(\frac{1}{5}) + \frac{(x)(0)}{(\frac{1}{5})})))sec(x{\frac{1}{5}}^{x}) + cos^{2}(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x})tan(x{\frac{1}{5}}^{x})({\frac{1}{5}}^{x} + x({\frac{1}{5}}^{x}((1)ln(\frac{1}{5}) + \frac{(x)(0)}{(\frac{1}{5})})))\\=&-2 * {\frac{1}{5}}^{x}sin(x{\frac{1}{5}}^{x})cos(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x}) - 2x{\frac{1}{5}}^{x}ln(\frac{1}{5})sin(x{\frac{1}{5}}^{x})cos(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x}) + {\frac{1}{5}}^{x}cos^{2}(x{\frac{1}{5}}^{x})tan(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x}) + x{\frac{1}{5}}^{x}ln(\frac{1}{5})cos^{2}(x{\frac{1}{5}}^{x})tan(x{\frac{1}{5}}^{x})sec(x{\frac{1}{5}}^{x})\\ \end{split}\end{equation} \]

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