If 2 functions are inverses of each other, then are their derivatives inverses of each other aswell

I need to know if i can infer this for my assignment where g(x) is the inverse of F(x) where
F(x)=6x^3 +7x - 3
The question states find G(10) which I calculated to be 1
and G'(10)

no

For an example, the derivative of sine is cosine, but the derivative of arcsine (or invsine, or sin^-1) is 1/(1 - x^2)^0.5, not arccos.

It's awfully messy; http://calculator.tutorvista.c… shows what G(x) is. How did you get the value of G(10)?

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or just use the formula on the following page:
http://oregonstate.edu/instruc…

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try this hypothetical f(x)= x^2
f'(x)=2x
then
f(x)=x^-2
f'(x)= -2x^-3
so inverse functions do not have inverse derivatives