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

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