Question

Please help! Find the 50th derivative of y=cos2x

Answer 1

what is the 50th derivative of cosine?

Answer 2

cosx

Answer 3

I think a little induction from following the pattern of the first 4 or 5 derivatives will point the way.

Answer 4

\[f'=-\sin(x)\]
\[f''=-\cos(x)\]
\[f^{(3)}=-\sin(x)\]
\[f^{(4)}=\cos(x)\] divide 50 by 4, get a remainder of 2, so looks like you are at \(-\cos(x)\) but of course you have the chain rule to consider
each time you take the derivative you will get another factor of 2 out front

Answer 5

in other words your coefficient will be \(2^{50}\)

Answer 6

Thanks!