How would the equation be written for the nth derivative? I understand it will be different for odd dertivatives and even derivatives. I'm working on f(x)= sin (3x) and I cannot figure out how to write the equation to the nth derivative.(adsbygoogle = window.adsbygoogle || []).push({});

f'(x) = 3cos(3x) 1st derivative

f"(x) = -9sin(3x) 2nd derivative

f"'(x) = -27cos(3x) 3rd derivative

f""(x) = 81sin(3x) 4th derivative.

so for the odd nth derivatives of f(x), I have come up with something like:

(-1) 3^n cos(3x)

and for the even nth derivatives of f(x), I have come up with something like:

(-1) 3^n sin(3x)

but it's just not right. How do I get alternating signs in this formula?

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# Higher Derivatives to the nth

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