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

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