There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ (({(\frac{(2 + cos(x))}{3})}^{x}) - 1){\frac{1}{x}}^{3}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{(\frac{1}{3}cos(x) + \frac{2}{3})^{x}}{x^{3}} - \frac{1}{x^{3}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{(\frac{1}{3}cos(x) + \frac{2}{3})^{x}}{x^{3}} - \frac{1}{x^{3}}\right)}{dx}\\=&\frac{-3(\frac{1}{3}cos(x) + \frac{2}{3})^{x}}{x^{4}} + \frac{((\frac{1}{3}cos(x) + \frac{2}{3})^{x}((1)ln(\frac{1}{3}cos(x) + \frac{2}{3}) + \frac{(x)(\frac{1}{3}*-sin(x) + 0)}{(\frac{1}{3}cos(x) + \frac{2}{3})}))}{x^{3}} - \frac{-3}{x^{4}}\\=&\frac{(\frac{1}{3}cos(x) + \frac{2}{3})^{x}ln(\frac{1}{3}cos(x) + \frac{2}{3})}{x^{3}} - \frac{3(\frac{1}{3}cos(x) + \frac{2}{3})^{x}}{x^{4}} - \frac{(\frac{1}{3}cos(x) + \frac{2}{3})^{x}sin(x)}{3(\frac{1}{3}cos(x) + \frac{2}{3})x^{2}} + \frac{3}{x^{4}}\\ \end{split}\end{equation} \]

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