Need help Differentiate z(t) = e^mt*cosnt

Question

anonymous · Answer

I know you need f(x) = e^mt fprime(x) = ?
g(x) = cosnt gprime(x) = ?
then use the product rule fgprime + gfprime

tkhunny · Answer

Is that $z(t) = e^{mt}\cos(nt)$?

anonymous · Answer

yeah is cosnt the same as cos(nt)?

tkhunny · Answer

I don't like it at all without the parentheses, but it is often understood correctly that way.  I would start using the notation that is most clear - use the parentheses.

tkhunny · Answer

I guess it's possible you mean $\cos^{n}(t)$.  Do you?

anonymous · Answer

Ah nope on the worksheet its just cosnt so i assume its cos(nt) like you said

tkhunny · Answer

See how it is ambiguous without the parentheses?  It's important to write clearly.

Well, you have chain rules and a product rule in your future.  What's your first attempt?

anonymous · Answer

Oh chain rule also? I thought it was just the product and I was doing (cos(nt))(me^mt)+(e^mt)(sin(nt))

tkhunny · Answer

Pretty close!  $\dfrac{d}{dt}\cos(nt) = -n\cdot\sin(nt)$ -- More chain rule and you missed the sign.