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

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