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

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