There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {(x + 1)}^{2}{e}^{x}(x + 4)\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = x^{3}{e}^{x} + 6x^{2}{e}^{x} + 9x{e}^{x} + 4{e}^{x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( x^{3}{e}^{x} + 6x^{2}{e}^{x} + 9x{e}^{x} + 4{e}^{x}\right)}{dx}\\=&3x^{2}{e}^{x} + x^{3}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 6*2x{e}^{x} + 6x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 9{e}^{x} + 9x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 4({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&9x^{2}{e}^{x} + 21x{e}^{x} + 13{e}^{x} + x^{3}{e}^{x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 9x^{2}{e}^{x} + 21x{e}^{x} + 13{e}^{x} + x^{3}{e}^{x}\right)}{dx}\\=&9*2x{e}^{x} + 9x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 21{e}^{x} + 21x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 13({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 3x^{2}{e}^{x} + x^{3}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&39x{e}^{x} + 34{e}^{x} + 12x^{2}{e}^{x} + x^{3}{e}^{x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 39x{e}^{x} + 34{e}^{x} + 12x^{2}{e}^{x} + x^{3}{e}^{x}\right)}{dx}\\=&39{e}^{x} + 39x({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 34({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 12*2x{e}^{x} + 12x^{2}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)})) + 3x^{2}{e}^{x} + x^{3}({e}^{x}((1)ln(e) + \frac{(x)(0)}{(e)}))\\=&73{e}^{x} + 63x{e}^{x} + 15x^{2}{e}^{x} + x^{3}{e}^{x}\\ \end{split}\end{equation} \]

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