There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ ln(x) + \frac{(4 + 11x)}{(24{x}^{2} + 24x)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = ln(x) + \frac{11x}{(24x^{2} + 24x)} + \frac{4}{(24x^{2} + 24x)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( ln(x) + \frac{11x}{(24x^{2} + 24x)} + \frac{4}{(24x^{2} + 24x)}\right)}{dx}\\=&\frac{1}{(x)} + 11(\frac{-(24*2x + 24)}{(24x^{2} + 24x)^{2}})x + \frac{11}{(24x^{2} + 24x)} + 4(\frac{-(24*2x + 24)}{(24x^{2} + 24x)^{2}})\\=&\frac{1}{x} - \frac{528x^{2}}{(24x^{2} + 24x)^{2}} - \frac{456x}{(24x^{2} + 24x)^{2}} + \frac{11}{(24x^{2} + 24x)} - \frac{96}{(24x^{2} + 24x)^{2}}\\ \end{split}\end{equation} \]

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