derivative of trig function

**calcnewbie** · September 29th 2008, 04:38 PM

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!

**Jhevon** · September 29th 2008, 04:45 PM

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

**calcnewbie** · September 29th 2008, 05:45 PM

Ok I'll give it a shot. Thx!

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