There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(ax*3 + bx*2 + cx + d)}{(e^{x}*3 + fx*2 + gx + h)}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{3ax}{(3e^{x} + 2fx + gx + h)} + \frac{2bx}{(3e^{x} + 2fx + gx + h)} + \frac{cx}{(3e^{x} + 2fx + gx + h)} + \frac{d}{(3e^{x} + 2fx + gx + h)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{3ax}{(3e^{x} + 2fx + gx + h)} + \frac{2bx}{(3e^{x} + 2fx + gx + h)} + \frac{cx}{(3e^{x} + 2fx + gx + h)} + \frac{d}{(3e^{x} + 2fx + gx + h)}\right)}{dx}\\=&3(\frac{-(3e^{x} + 2f + g + 0)}{(3e^{x} + 2fx + gx + h)^{2}})ax + \frac{3a}{(3e^{x} + 2fx + gx + h)} + 2(\frac{-(3e^{x} + 2f + g + 0)}{(3e^{x} + 2fx + gx + h)^{2}})bx + \frac{2b}{(3e^{x} + 2fx + gx + h)} + (\frac{-(3e^{x} + 2f + g + 0)}{(3e^{x} + 2fx + gx + h)^{2}})cx + \frac{c}{(3e^{x} + 2fx + gx + h)} + (\frac{-(3e^{x} + 2f + g + 0)}{(3e^{x} + 2fx + gx + h)^{2}})d + 0\\=&\frac{-9axe^{x}}{(3e^{x} + 2fx + gx + h)^{2}} - \frac{6afx}{(3e^{x} + 2fx + gx + h)^{2}} - \frac{3agx}{(3e^{x} + 2fx + gx + h)^{2}} + \frac{3a}{(3e^{x} + 2fx + gx + h)} - \frac{6bxe^{x}}{(3e^{x} + 2fx + gx + h)^{2}} - \frac{4bfx}{(3e^{x} + 2fx + gx + h)^{2}} - \frac{2bgx}{(3e^{x} + 2fx + gx + h)^{2}} + \frac{2b}{(3e^{x} + 2fx + gx + h)} - \frac{3cxe^{x}}{(3e^{x} + 2fx + gx + h)^{2}} - \frac{2cfx}{(3e^{x} + 2fx + gx + h)^{2}} - \frac{cgx}{(3e^{x} + 2fx + gx + h)^{2}} + \frac{c}{(3e^{x} + 2fx + gx + h)} - \frac{3de^{x}}{(3e^{x} + 2fx + gx + h)^{2}} - \frac{2df}{(3e^{x} + 2fx + gx + h)^{2}} - \frac{dg}{(3e^{x} + 2fx + gx + h)^{2}}\\ \end{split}\end{equation} \]

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