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

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