# Thread: finding f'(x) of a certain integral when x > 1?

1. ## finding f'(x) of a certain integral when x > 1?

how do i find f'(x) if f(x) = (integral sqrt(lnx) on top 1 on bottom) e^(t^2) for x>1?

2. Originally Posted by Synth3t1c
how do i find f'(x) if f(x) = (integral sqrt(lnx) on top 1 on bottom) e^(t^2) for x>1?
Theorem (can be proved using chain rule and Fundamental Theorem of Calculus):

If $f(x) = \int_a^{g(x)} h(t) \, dt$ then $f'(x) = g'(x) \cdot h(g(x))$.