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Differentiate the function 
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#1
Nov2510, 09:26 AM

P: 726

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? 


#2
Nov2510, 09:47 AM

Mentor
P: 18,023

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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