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

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