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

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