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

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