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

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