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> Let $f(x)=(x-a)^ng(x)$ such that $g(a)\neq 0$; then I would like to compute the $n$-th derivative of $f$:
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$$f^{(n)}(x)=\dfrac{d^n}{dx^{n}}\Bigl((x-a)^n\cdot g(x) \Bigr)$$

Can I have any suggestion?