There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ a(1 + x)(b + cln(a(1 + x))) - \frac{a(b + cln(a(1 + x)))}{(1 - d)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = abx + acln(ax + a) + ab + acxln(ax + a) - \frac{ab}{(-d + 1)} - \frac{acln(ax + a)}{(-d + 1)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( abx + acln(ax + a) + ab + acxln(ax + a) - \frac{ab}{(-d + 1)} - \frac{acln(ax + a)}{(-d + 1)}\right)}{dx}\\=&ab + \frac{ac(a + 0)}{(ax + a)} + 0 + acln(ax + a) + \frac{acx(a + 0)}{(ax + a)} - (\frac{-(0 + 0)}{(-d + 1)^{2}})ab + 0 - (\frac{-(0 + 0)}{(-d + 1)^{2}})acln(ax + a) - \frac{ac(a + 0)}{(-d + 1)(ax + a)}\\=&ab + \frac{a^{2}cx}{(ax + a)} + acln(ax + a) + \frac{a^{2}c}{(ax + a)} - \frac{a^{2}c}{(ax + a)(-d + 1)}\\ \end{split}\end{equation} \]

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