There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ {(3x + 2)}^{5}{({x}^{3} - 2)}^{2}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = 243x^{11} - 252x^{8} + 810x^{10} - 3000x^{7} + 1080x^{9} - 1908x^{5} + 2280x^{4} - 4288x^{6} + 4192x^{3} + 2880x^{2} + 960x + 128\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( 243x^{11} - 252x^{8} + 810x^{10} - 3000x^{7} + 1080x^{9} - 1908x^{5} + 2280x^{4} - 4288x^{6} + 4192x^{3} + 2880x^{2} + 960x + 128\right)}{dx}\\=&243*11x^{10} - 252*8x^{7} + 810*10x^{9} - 3000*7x^{6} + 1080*9x^{8} - 1908*5x^{4} + 2280*4x^{3} - 4288*6x^{5} + 4192*3x^{2} + 2880*2x + 960 + 0\\=&2673x^{10} - 2016x^{7} + 8100x^{9} - 21000x^{6} + 9720x^{8} - 9540x^{4} + 9120x^{3} - 25728x^{5} + 12576x^{2} + 5760x + 960\\ \end{split}\end{equation} \]

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