There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({(\frac{{(x + 2)}^{1}}{2} - x)}^{8}){\frac{1}{(2x)}}^{1}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{\frac{1}{4}(\frac{-1}{2}x + 1)^{8}}{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{\frac{1}{4}(\frac{-1}{2}x + 1)^{8}}{x}\right)}{dx}\\=&\frac{\frac{1}{4}(8(\frac{-1}{2}x + 1)^{7}(\frac{-1}{2} + 0))}{x} + \frac{\frac{1}{4}(\frac{-1}{2}x + 1)^{8}*-1}{x^{2}}\\=&\frac{-(\frac{-1}{2}x + 1)^{7}}{x} - \frac{(\frac{-1}{2}x + 1)^{8}}{4x^{2}}\\ \end{split}\end{equation} \]

Your problem has not been solved here? Please take a look at the  hot problems ！