There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{(2{x}^{2} + 3x + 2)}{(2sqrt({x}^{2} + x + 1)sqrt({x}^{2} + 2x + 4))}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{x^{2}}{sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)} + \frac{\frac{3}{2}x}{sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)} + \frac{1}{sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{x^{2}}{sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)} + \frac{\frac{3}{2}x}{sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)} + \frac{1}{sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)}\right)}{dx}\\=&\frac{2x}{sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)} + \frac{x^{2}*-(2x + 1 + 0)*\frac{1}{2}}{(x^{2} + x + 1)(x^{2} + x + 1)^{\frac{1}{2}}sqrt(x^{2} + 2x + 4)} + \frac{x^{2}*-(2x + 2 + 0)*\frac{1}{2}}{sqrt(x^{2} + x + 1)(x^{2} + 2x + 4)(x^{2} + 2x + 4)^{\frac{1}{2}}} + \frac{\frac{3}{2}}{sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)} + \frac{\frac{3}{2}x*-(2x + 1 + 0)*\frac{1}{2}}{(x^{2} + x + 1)(x^{2} + x + 1)^{\frac{1}{2}}sqrt(x^{2} + 2x + 4)} + \frac{\frac{3}{2}x*-(2x + 2 + 0)*\frac{1}{2}}{sqrt(x^{2} + x + 1)(x^{2} + 2x + 4)(x^{2} + 2x + 4)^{\frac{1}{2}}} + \frac{-(2x + 1 + 0)*\frac{1}{2}}{(x^{2} + x + 1)(x^{2} + x + 1)^{\frac{1}{2}}sqrt(x^{2} + 2x + 4)} + \frac{-(2x + 2 + 0)*\frac{1}{2}}{sqrt(x^{2} + x + 1)(x^{2} + 2x + 4)(x^{2} + 2x + 4)^{\frac{1}{2}}}\\=&\frac{2x}{sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)} - \frac{x^{3}}{(x^{2} + x + 1)^{\frac{3}{2}}sqrt(x^{2} + 2x + 4)} - \frac{2x^{2}}{(x^{2} + x + 1)^{\frac{3}{2}}sqrt(x^{2} + 2x + 4)} - \frac{x^{3}}{(x^{2} + 2x + 4)^{\frac{3}{2}}sqrt(x^{2} + x + 1)} - \frac{5x^{2}}{2(x^{2} + 2x + 4)^{\frac{3}{2}}sqrt(x^{2} + x + 1)} + \frac{3}{2sqrt(x^{2} + x + 1)sqrt(x^{2} + 2x + 4)} - \frac{7x}{4(x^{2} + x + 1)^{\frac{3}{2}}sqrt(x^{2} + 2x + 4)} - \frac{5x}{2(x^{2} + 2x + 4)^{\frac{3}{2}}sqrt(x^{2} + x + 1)} - \frac{1}{2(x^{2} + x + 1)^{\frac{3}{2}}sqrt(x^{2} + 2x + 4)} - \frac{1}{(x^{2} + 2x + 4)^{\frac{3}{2}}sqrt(x^{2} + x + 1)}\\ \end{split}\end{equation} \]

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