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

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