There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(x + 1)}^{3}sqrt(x) - {\frac{1}{(x + 4)}}^{2}e^{x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{3}sqrt(x) + 3x^{2}sqrt(x) + 3xsqrt(x) + sqrt(x) - \frac{e^{x}}{(x + 4)^{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{3}sqrt(x) + 3x^{2}sqrt(x) + 3xsqrt(x) + sqrt(x) - \frac{e^{x}}{(x + 4)^{2}}\right)}{dx}\\=&3x^{2}sqrt(x) + \frac{x^{3}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 3*2xsqrt(x) + \frac{3x^{2}*\frac{1}{2}}{(x)^{\frac{1}{2}}} + 3sqrt(x) + \frac{3x*\frac{1}{2}}{(x)^{\frac{1}{2}}} + \frac{\frac{1}{2}}{(x)^{\frac{1}{2}}} - (\frac{-2(1 + 0)}{(x + 4)^{3}})e^{x} - \frac{e^{x}}{(x + 4)^{2}}\\=&3x^{2}sqrt(x) + 6xsqrt(x) + \frac{x^{\frac{5}{2}}}{2} + \frac{3x^{\frac{3}{2}}}{2} + 3sqrt(x) + \frac{3x^{\frac{1}{2}}}{2} + \frac{1}{2x^{\frac{1}{2}}} + \frac{2e^{x}}{(x + 4)^{3}} - \frac{e^{x}}{(x + 4)^{2}}\\ \end{split}\end{equation} \]

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