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

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