Let $f(x) = \int_1 ^x g(k) dk$ and $g(t) = \int_0 ^{4\tan(t)} \sqrt{ 16 + w² } dw$ Determine the correct value of $f''(\frac{\pi}{4})$.
I know how to solve this by solving for $g(t)$. Then I know that $f'(x) = g(x)$; $f''(x) = g'(x)$ and I get my answer. I want to know if there is another way to get to the answer without doing all that work?
