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?
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
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
Hopefully this helps!