Differentiate the function

by JG89
Tags: differentiate, function
JG89 is offline
Nov25-10, 09:26 AM
P: 724
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?
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Nov25-10, 09:47 AM
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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".

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