Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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?

share|cite|improve this question
Why do you think that is not correct? I'd say it is, assuming the limit exists. – DonAntonio Nov 7 '12 at 23:12
Probably, they wanted to express $(f^{-1})'$ using $f'$ and $f$.. – Berci Nov 7 '12 at 23:34
@berci I think you are correct. – yiyi Nov 8 '12 at 0:50
up vote 3 down vote accepted

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 $$ h = (x+h)-x = f(y+t) -f(y) $$

share|cite|improve this answer
thanks, I will try to work that path out. – yiyi Nov 8 '12 at 0:51

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.