d/dx integral (f^-1 (t) dt) the boundaries are 0 to f(x).

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- December 4th 2006, 01:47 PMmyoplex11FTOcalculus simplification problem
d/dx integral (f^-1 (t) dt) the boundaries are 0 to f(x).

- December 4th 2006, 04:31 PMThePerfectHacker
What makes so angry these problem do not mention intervals of a bijection map, continuity, definess, differenciability,.... Makes me so angry. I JUST CANNOT DO PROBLEMS LIKE THIS. So I am going to assume you have a differenciable and invertible function over the entire number line.

I presume you mean,

Then you can view as a composition,

Where,

Thus,

is differenciable.

Thus we can use chain rule theorem,

But by fundamental theorem,

Thus,

But,

the identity map.

Thus,