How to find $\frac{d^n}{dx^n} e^x\cos x$ How can I get a formula for the n-th derivative of this function? I know that it cycles every 4 derivatives with a factor of $-4$. $e^x(\cos x-\sin x) \to e^x(-2\sin x) \to -2e^x(\sin x+\cos x) \to -4e^x\cos x$

You can always use Leibniz rule. It is hassle free abd easy to use. It also gives you an idea of writing your results in generalized forms.
