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

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