Question

whats the nth derivative of cos3x

Answer 1

Well we know this as the chain rule

\[\large f(x) = cos(3x)\]
\[\large f'(x) = -3sin(3x)\]
\[\large f''(x) = -9cos(3x)\]
\[\large f'''(x) = 27sin(3x)\]
\[\large f^{4}(x) = 81cos(3x)\]

And it repeats from there cycling through sin and cos...so what can we assume about the rule?