There are 1 questions in this calculation: for each question, the 1 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ first\ derivative\ of\ function\ x(1 - x)({x}^{4} + {(1 - x)}^{4})\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = - 2x^{6} + 6x^{5} - 10x^{4} + 10x^{3} - 5x^{2} + x\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( - 2x^{6} + 6x^{5} - 10x^{4} + 10x^{3} - 5x^{2} + x\right)}{dx}\\=& - 2*6x^{5} + 6*5x^{4} - 10*4x^{3} + 10*3x^{2} - 5*2x + 1\\=& - 12x^{5} + 30x^{4} - 40x^{3} + 30x^{2} - 10x + 1\\ \end{split}\end{equation} \]

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