1. The problem statement, all variables and given/known data If [tex] f(x) = \int_{x^2}^{3x} \sqrt{t^3 + x^3} dt [/tex] then find the expression for f'(x) 2. Relevant equations 3. The attempt at a solution Usually I would use the FTC, but since there the variable x occurs in the integrand, I don't know how to differentiate this. Any help?
The standard way of doing this is by the Leibniz rule. See http://en.wikipedia.org/wiki/Leibniz_integral_rule under the section "variable limits".