- #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?