Taylor made

Calculus Level 5

Find f(2016)(0)2016!\dfrac{f^{(2016)}(0)}{2016!} for f(x)=x3(1x)3(1+x+x2)f(x)=\dfrac{x^3}{(1-x)^3(1+x+x^2)}.

Clarifications:

  • f(k)(x)f^{(k)}(x) denotes the kthk^\text{th} derivative of f(x)f(x) .

  • !! denotes the factorial notation. For example, 8!=1×2×3××88! = 1\times2\times3\times\cdots\times8 .

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