Question

Find f^(302)(x) where f(x) = cos(5x). You do not need to simplify your
answer.

Answer 1

302/4 = 75 r 2

The original equation and it's first 4 derivatives.

\(f^{[0]} = \cos(5x)\)
\(f^{[1]} = -5\sin(5x)\)
\(f^{[2]} = -5^{2}\cos(5x)\)
\(f^{[3]} = 5^{3}\sin(5x)\)
\(f^{[4]} = 5^{4}\cos(5x)\)

Find a pattern and exploit it.