There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ lg(x) - \frac{(\frac{(-x - 1)}{x} + 1)x}{6}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg(x) + \frac{1}{6}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(x) + \frac{1}{6}\right)}{dx}\\=&\frac{1}{ln{10}(x)} + 0\\=&\frac{1}{xln{10}}\\ \end{split}\end{equation} \]

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