If f(x)=(4x^2tan(x))/(sec(x), how do I find f'(x) and f'(3)?

I tried finding f'(x) first, but my answer of (8xsec^2(x)(sec(x))-(4x^2tan(x)(sec(x)tan(x))))/(secx)^2 is incorrect. Do you have to do something other than the quotient rule or did I just do my math wrong?

1 Answer
Mar 7, 2018

f'(x) = 8xsinx + 4x^2cosx

Explanation:

We can rewrite as

f(x) = 4x^2tanx(1/secx)

f(x) = 4x^2tanx(1/(1/cosx))

f(x) = 4x^2tanxcosx

f(x) = 4x^2sinx

Now we can easily differentiate using the product rule.

f'(x) = 8x(sinx) + cosx(4x^2)

f'(x) = 8xsinx + 4x^2cosx

I'll let you evaluate f'(3).

Hopefully this helps!