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

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