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

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