There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(144e{x}^{5} - 48{e}^{3}x - 96{x}^{3}{e}^{2})}{(3{x}^{2} + {e}^{4})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{144x^{5}e}{(3x^{2} + e^{4})} - \frac{48xe^{3}}{(3x^{2} + e^{4})} - \frac{96x^{3}e^{2}}{(3x^{2} + e^{4})}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{144x^{5}e}{(3x^{2} + e^{4})} - \frac{48xe^{3}}{(3x^{2} + e^{4})} - \frac{96x^{3}e^{2}}{(3x^{2} + e^{4})}\right)}{dx}\\=&144(\frac{-(3*2x + 4e^{3}*0)}{(3x^{2} + e^{4})^{2}})x^{5}e + \frac{144*5x^{4}e}{(3x^{2} + e^{4})} + \frac{144x^{5}*0}{(3x^{2} + e^{4})} - 48(\frac{-(3*2x + 4e^{3}*0)}{(3x^{2} + e^{4})^{2}})xe^{3} - \frac{48e^{3}}{(3x^{2} + e^{4})} - \frac{48x*3e^{2}*0}{(3x^{2} + e^{4})} - 96(\frac{-(3*2x + 4e^{3}*0)}{(3x^{2} + e^{4})^{2}})x^{3}e^{2} - \frac{96*3x^{2}e^{2}}{(3x^{2} + e^{4})} - \frac{96x^{3}*2e*0}{(3x^{2} + e^{4})}\\=&\frac{-864x^{6}e}{(3x^{2} + e^{4})^{2}} + \frac{720x^{4}e}{(3x^{2} + e^{4})} + \frac{288x^{2}e^{3}}{(3x^{2} + e^{4})^{2}} - \frac{48e^{3}}{(3x^{2} + e^{4})} + \frac{576x^{4}e^{2}}{(3x^{2} + e^{4})^{2}} - \frac{288x^{2}e^{2}}{(3x^{2} + e^{4})}\\ \end{split}\end{equation} \]

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