There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{-4x}{5} + \frac{5}{x} + 4ln(\frac{{({x}^{2})}^{\frac{1}{2}}}{3}) + \frac{86}{15}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{-4}{5}x + \frac{5}{x} + 4ln(\frac{1}{3}x) + \frac{86}{15}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{-4}{5}x + \frac{5}{x} + 4ln(\frac{1}{3}x) + \frac{86}{15}\right)}{dx}\\=&\frac{-4}{5} + \frac{5*-1}{x^{2}} + \frac{4*\frac{1}{3}}{(\frac{1}{3}x)} + 0\\=& - \frac{5}{x^{2}} + \frac{4}{x} - \frac{4}{5}\\ \end{split}\end{equation} \]

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