1. derivative of trig function

I cannot seem to come up with a correct answer for this:

Find the derivative of f when

f(x)= 3 tan 4x cos^3 4x

The answer choices are all in sin and cos, and I seem to keep getting an answer as a fraction, but that is not a choice in any answer. Any help/advice would be greatly appreciated. Thx!

2. Originally Posted by calcnewbie
I cannot seem to come up with a correct answer for this:

Find the derivative of f when

f(x)= 3 tan 4x cos^3 4x

The answer choices are all in sin and cos, and I seem to keep getting an answer as a fraction, but that is not a choice in any answer. Any help/advice would be greatly appreciated. Thx!
if all the answers are in sines and cosines then switch to sines and cosines

$f(x) = 3 \tan 4x \cos^3 4x = 3 \frac {\sin 4x}{\cos 4x} \cdot \cos^3 4x = 3 \sin 4x \cos^2 4x$

we could change this to purely sines, but since cosines are in the answer, lets not do that

now use the product rule (and the chain rule) to find the derivative

3. Ok I'll give it a shot. Thx!