Im not sure if there is a typo, or I'm just not seeing how to solve this:

help please (:

Compute the derivative w.r.t. t of g(t) := ∫_{0}^{t }f(t,x) dx.

sorry for the iffy notation

Printable View

- December 4th 2012, 07:09 AMMaroka93Help computing derivative of a 2 variable integral
Im not sure if there is a typo, or I'm just not seeing how to solve this:

help please (:

Compute the derivative w.r.t. t of g(t) := ∫_{0}^{t }f(t,x) dx.

sorry for the iffy notation - December 4th 2012, 11:03 AMTriKriRe: Help computing derivative of a 2 variable integral
Use the definition of the derivative:

You see that the first term in the fraction can be written as

From there it should be an easy task to escape the limit formulation and obtain the derivative.

Good luck! - December 8th 2012, 07:17 AMTriKriRe: Help computing derivative of a 2 variable integral
Had any luck solving the problem yet?

- December 8th 2012, 08:07 AMHallsofIvyRe: Help computing derivative of a 2 variable integral
I would recommend "Leibniz' rule" which generalizes the "Fundamental Theorem of Calculus":

- December 8th 2012, 12:03 PMTriKriRe: Help computing derivative of a 2 variable integral
I think that should be

- December 8th 2012, 12:05 PMHallsofIvyRe: Help computing derivative of a 2 variable integral
Yes, you are right. I forgot the derivatives of u and v. Thanks.