There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ lg(lg(x*1000 + 40)*\frac{11}{2})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = lg(\frac{11}{2}lg(1000x + 40))\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( lg(\frac{11}{2}lg(1000x + 40))\right)}{dx}\\=&\frac{\frac{11}{2}(1000 + 0)}{ln{10}(\frac{11}{2}lg(1000x + 40))ln{10}(1000x + 40)}\\=&\frac{1000}{(1000x + 40)ln^{2}{10}lg(1000x + 40)}\\ \end{split}\end{equation} \]

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