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

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