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

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