There are 1 questions in this calculation: for each question, the 4 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ 4th\ derivative\ of\ function\ 3xxe^{xxx + 2x} + 2e^{xxx + 2x}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 3x^{2}e^{x^{3} + 2x} + 2e^{x^{3} + 2x}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 3x^{2}e^{x^{3} + 2x} + 2e^{x^{3} + 2x}\right)}{dx}\\=&3*2xe^{x^{3} + 2x} + 3x^{2}e^{x^{3} + 2x}(3x^{2} + 2) + 2e^{x^{3} + 2x}(3x^{2} + 2)\\=&6xe^{x^{3} + 2x} + 9x^{4}e^{x^{3} + 2x} + 12x^{2}e^{x^{3} + 2x} + 4e^{x^{3} + 2x}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 6xe^{x^{3} + 2x} + 9x^{4}e^{x^{3} + 2x} + 12x^{2}e^{x^{3} + 2x} + 4e^{x^{3} + 2x}\right)}{dx}\\=&6e^{x^{3} + 2x} + 6xe^{x^{3} + 2x}(3x^{2} + 2) + 9*4x^{3}e^{x^{3} + 2x} + 9x^{4}e^{x^{3} + 2x}(3x^{2} + 2) + 12*2xe^{x^{3} + 2x} + 12x^{2}e^{x^{3} + 2x}(3x^{2} + 2) + 4e^{x^{3} + 2x}(3x^{2} + 2)\\=&14e^{x^{3} + 2x} + 54x^{3}e^{x^{3} + 2x} + 36xe^{x^{3} + 2x} + 27x^{6}e^{x^{3} + 2x} + 54x^{4}e^{x^{3} + 2x} + 36x^{2}e^{x^{3} + 2x}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 14e^{x^{3} + 2x} + 54x^{3}e^{x^{3} + 2x} + 36xe^{x^{3} + 2x} + 27x^{6}e^{x^{3} + 2x} + 54x^{4}e^{x^{3} + 2x} + 36x^{2}e^{x^{3} + 2x}\right)}{dx}\\=&14e^{x^{3} + 2x}(3x^{2} + 2) + 54*3x^{2}e^{x^{3} + 2x} + 54x^{3}e^{x^{3} + 2x}(3x^{2} + 2) + 36e^{x^{3} + 2x} + 36xe^{x^{3} + 2x}(3x^{2} + 2) + 27*6x^{5}e^{x^{3} + 2x} + 27x^{6}e^{x^{3} + 2x}(3x^{2} + 2) + 54*4x^{3}e^{x^{3} + 2x} + 54x^{4}e^{x^{3} + 2x}(3x^{2} + 2) + 36*2xe^{x^{3} + 2x} + 36x^{2}e^{x^{3} + 2x}(3x^{2} + 2)\\=&276x^{2}e^{x^{3} + 2x} + 64e^{x^{3} + 2x} + 324x^{5}e^{x^{3} + 2x} + 432x^{3}e^{x^{3} + 2x} + 144xe^{x^{3} + 2x} + 81x^{8}e^{x^{3} + 2x} + 216x^{6}e^{x^{3} + 2x} + 216x^{4}e^{x^{3} + 2x}\\\\ &\color{blue}{The\ 4th\ derivative\ of\ function:} \\&\frac{d\left( 276x^{2}e^{x^{3} + 2x} + 64e^{x^{3} + 2x} + 324x^{5}e^{x^{3} + 2x} + 432x^{3}e^{x^{3} + 2x} + 144xe^{x^{3} + 2x} + 81x^{8}e^{x^{3} + 2x} + 216x^{6}e^{x^{3} + 2x} + 216x^{4}e^{x^{3} + 2x}\right)}{dx}\\=&276*2xe^{x^{3} + 2x} + 276x^{2}e^{x^{3} + 2x}(3x^{2} + 2) + 64e^{x^{3} + 2x}(3x^{2} + 2) + 324*5x^{4}e^{x^{3} + 2x} + 324x^{5}e^{x^{3} + 2x}(3x^{2} + 2) + 432*3x^{2}e^{x^{3} + 2x} + 432x^{3}e^{x^{3} + 2x}(3x^{2} + 2) + 144e^{x^{3} + 2x} + 144xe^{x^{3} + 2x}(3x^{2} + 2) + 81*8x^{7}e^{x^{3} + 2x} + 81x^{8}e^{x^{3} + 2x}(3x^{2} + 2) + 216*6x^{5}e^{x^{3} + 2x} + 216x^{6}e^{x^{3} + 2x}(3x^{2} + 2) + 216*4x^{3}e^{x^{3} + 2x} + 216x^{4}e^{x^{3} + 2x}(3x^{2} + 2)\\=&840xe^{x^{3} + 2x} + 2880x^{4}e^{x^{3} + 2x} + 2040x^{2}e^{x^{3} + 2x} + 272e^{x^{3} + 2x} + 1620x^{7}e^{x^{3} + 2x} + 3240x^{5}e^{x^{3} + 2x} + 2160x^{3}e^{x^{3} + 2x} + 243x^{10}e^{x^{3} + 2x} + 810x^{8}e^{x^{3} + 2x} + 1080x^{6}e^{x^{3} + 2x}\\ \end{split}\end{equation} \]

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