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 was wondering if it there is a function $f:\mathbb{R} \rightarrow \mathbb{R}$ that is differentiable everywhere, but with a derivitive that is nowhere differentiable.

share|cite|improve this question
You could integrate the Weierstrass function. – Dylan Moreland Feb 25 '12 at 6:05
up vote 5 down vote accepted

Look up your favorite example of a continuous-but-nowhere differentiable function, then integrate it. By the fundamental theorem of calculus you'll get the original function back when you differentiate.

share|cite|improve this answer

Yes, there is. Let $g$ be the Weierstrass function, and put $$ f(x)=\int_0^x g(t)dt. $$ Then $f$ is everywhere differentiable because it is an integral of a continuous function. But $f'=g$, which is nowhere differentiable.

share|cite|improve this answer
Beaten to the punch! +1 – Alex Becker Feb 25 '12 at 6:07
Oh, right. That's pretty cool. Thanks – Chris Dugale Feb 25 '12 at 17:15

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.