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I have tried using the definition of derivative by

$ \lim_{h \to 0} \dfrac{f^{-1}\left(x + h\right) - f^{-1}\left(x\right)}{h} $

but that is not correct. (it was marked wrong).

What did I do wrong?

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    @berci I think you are correct.2012-11-08

1 Answers 1

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This is correct so far, but you should go on, somehow introducing the definition of $f'$.

Briefly, it goes like $t:=f^{-1}(x+h)-f^{-1}(x)$, we need that $t\to 0$ as $h\to 0$, and then consider $y:=f^{-1}(x)$ and $ h = (x+h)-x = f(y+t) -f(y) $

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    thanks, I will try to work that path out.2012-11-08