There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ \frac{({x}^{3} + 3{x}^{2}){(x + 1)}^{2}}{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = \frac{1}{2}x^{5} + \frac{5}{2}x^{4} + \frac{7}{2}x^{3} + \frac{3}{2}x^{2}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( \frac{1}{2}x^{5} + \frac{5}{2}x^{4} + \frac{7}{2}x^{3} + \frac{3}{2}x^{2}\right)}{dx}\\=&\frac{1}{2}*5x^{4} + \frac{5}{2}*4x^{3} + \frac{7}{2}*3x^{2} + \frac{3}{2}*2x\\=&\frac{5x^{4}}{2} + 10x^{3} + \frac{21x^{2}}{2} + 3x\\ \end{split}\end{equation} \]

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