PhysicsIzHard
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Homework Statement
Use the definition of the derivative to show that if G(x)=\int^{u(x)}_{a}f(z)dz, then \frac{dG}{dx}=f(u(x))\frac{du}{dx}. This is called Leibniz's rule.
Also, by thinking of the value of an integral as the area under the curve of the integrand (and drawing a picture of that area), convince yourself that the following is true: lim\underline{x\rightarrow0}\int^{a+x}_{a}f(z)dz=lim\underline{x\rightarrow0}f(a)\int^{a+x}_{a}dz. A relation like this will probably be useful in your solution to this problem.
Homework Equations
http://upload.wikimedia.org/math/4/2/c/42cf4f4861ae1266b13104c4115e7b5d.png
The Attempt at a Solution
I have tried to sub G(x) into the definition of the derivative equation but that gets me no where. Any ideas anyone on where to start this?