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

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