- #1

PhysicsIzHard

- 9

- 0

## Homework Statement

Use the definition of the derivative to show that if G(x)=[itex]\int[/itex][itex]^{u(x)}_{a}[/itex]

*f(z)dz*, then [itex]\frac{dG}{dx}[/itex]=f(u(x))[itex]\frac{du}{dx}[/itex]. 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[itex]\underline{x\rightarrow0}[/itex][itex]\int[/itex][itex]^{a+x}_{a}[/itex]

*f(z)dz*=lim[itex]\underline{x\rightarrow0}[/itex]

*f(a)*[itex]\int[/itex][itex]^{a+x}_{a}[/itex]

*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?