How Do You Differentiate an Integral with Variable Limits and Parameters?

[JG89]

Homework Statement

If $$f(x) = \int_{x^2}^{3x} \sqrt{t^3 + x^3} dt$$ then find the expression for f'(x)

Homework Equations

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?

 

[micromass]

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".