# Think outside the box

Calculus Level 4

Let $$f^{(0)}(x) = (1+2x-x^2)^4$$, where $$f^{(n)}(x)$$ denotes the $$n^\text{th}$$ derivative of $$f(x)$$. If the value of $$f^{(7)}(0)$$ is in the form $$-k!$$, where $$k$$ is a natural number, find the value of $$k$$.

Notation: $$!$$ is the factorial notation. For example, $$8! = 1\times2\times3\times\cdots\times8$$.

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