There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ sqrt(x + 1)(x + 2)(2x + 1)(2x + 3)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 4x^{3}sqrt(x + 1) + 16x^{2}sqrt(x + 1) + 19xsqrt(x + 1) + 6sqrt(x + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 4x^{3}sqrt(x + 1) + 16x^{2}sqrt(x + 1) + 19xsqrt(x + 1) + 6sqrt(x + 1)\right)}{dx}\\=&4*3x^{2}sqrt(x + 1) + \frac{4x^{3}(1 + 0)*\frac{1}{2}}{(x + 1)^{\frac{1}{2}}} + 16*2xsqrt(x + 1) + \frac{16x^{2}(1 + 0)*\frac{1}{2}}{(x + 1)^{\frac{1}{2}}} + 19sqrt(x + 1) + \frac{19x(1 + 0)*\frac{1}{2}}{(x + 1)^{\frac{1}{2}}} + \frac{6(1 + 0)*\frac{1}{2}}{(x + 1)^{\frac{1}{2}}}\\=&12x^{2}sqrt(x + 1) + \frac{2x^{3}}{(x + 1)^{\frac{1}{2}}} + 32xsqrt(x + 1) + \frac{8x^{2}}{(x + 1)^{\frac{1}{2}}} + 19sqrt(x + 1) + \frac{19x}{2(x + 1)^{\frac{1}{2}}} + \frac{3}{(x + 1)^{\frac{1}{2}}}\\ \end{split}\end{equation} \]

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