There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ x(x + sqrt(x*2 + 1))(x*2 + 1)*12 + (x + sqrt(x*2 + 1))\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 24x^{2}sqrt(2x + 1) + 12xsqrt(2x + 1) + 12x^{2} + 24x^{3} + x + sqrt(2x + 1)\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 24x^{2}sqrt(2x + 1) + 12xsqrt(2x + 1) + 12x^{2} + 24x^{3} + x + sqrt(2x + 1)\right)}{dx}\\=&24*2xsqrt(2x + 1) + \frac{24x^{2}(2 + 0)*\frac{1}{2}}{(2x + 1)^{\frac{1}{2}}} + 12sqrt(2x + 1) + \frac{12x(2 + 0)*\frac{1}{2}}{(2x + 1)^{\frac{1}{2}}} + 12*2x + 24*3x^{2} + 1 + \frac{(2 + 0)*\frac{1}{2}}{(2x + 1)^{\frac{1}{2}}}\\=&48xsqrt(2x + 1) + \frac{24x^{2}}{(2x + 1)^{\frac{1}{2}}} + 12sqrt(2x + 1) + \frac{12x}{(2x + 1)^{\frac{1}{2}}} + 24x + 72x^{2} + \frac{1}{(2x + 1)^{\frac{1}{2}}} + 1\\ \end{split}\end{equation} \]

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