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\(\displaystyle f(x)=x\sin(x)\)

Derive a formula for:

\(\displaystyle f^{(n)}(x)\)

Using this, infer a formula for:

\(\displaystyle \frac{d^n}{dx^n}\left(x\cos(x) \right)\)

edit: I wanted to make sure it is clearly understood that:

\(\displaystyle f^{(n)}(x)\equiv\frac{d^n}{dx^n}\left(f(x) \right)\)