There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(sqrt(x)) + {x}^{x} + sqrt(lg(sqrt(x)))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(sqrt(x)) + {x}^{x} + sqrt(lg(sqrt(x)))\right)}{dx}\\=&\frac{\frac{1}{2}}{(sqrt(x))(x)^{\frac{1}{2}}} + ({x}^{x}((1)ln(x) + \frac{(x)(1)}{(x)})) + \frac{\frac{1}{2}*\frac{1}{2}}{ln{10}(sqrt(x))(x)^{\frac{1}{2}}(lg(sqrt(x)))^{\frac{1}{2}}}\\=&\frac{1}{2x^{\frac{1}{2}}sqrt(x)} + {x}^{x}ln(x) + {x}^{x} + \frac{1}{4x^{\frac{1}{2}}ln{10}lg^{\frac{1}{2}}(sqrt(x))sqrt(x)}\\ \end{split}\end{equation} \]

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