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

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