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

Your problem has not been solved here? Please take a look at the  hot problems ！