I need to find the derivative of an integral, with a limit of integration being a function:

How do I find g'(x)?

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- May 16th 2010, 10:56 AMAlderDragonDerivative of an Integral problem
I need to find the derivative of an integral, with a limit of integration being a function:

How do I find g'(x)? - May 16th 2010, 11:16 AMCaptainBlack
- May 16th 2010, 06:49 PMAlderDragon
Upon closer inspection of my past work I found another method of doing this type of problem. Substitute in for and multiply by the derivative of , :

Is this the correct answer? And, if so, is this a different answer than you might obtain using a different method? - May 16th 2010, 08:42 PMCaptainBlack
- May 17th 2010, 04:18 AMHallsofIvy
By the way, here is the general Leibniz formula:

.

It can be proved from the fundamental theorem of calculus and using the chain rule for both the upper and lower limits.