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

What is the difference between Complex derivative and Complex differentiability? And if they are different how you define Complex derivative? Is it same as definition of complex differentiability?

share|cite|improve this question
If a function is complex differentiable at a point, then it has a complex derivative at that point.... – Euler....IS_ALIVE Aug 27 '12 at 16:30
Same thing basically. A functions is 'complex differentiable' iff it has a complex derivative (over $\mathbb{C}$). Generally the point is that being differentiable over $\mathbb{C}$ is a lot stronger than being differentiable over $\mathbb{R}$. – copper.hat Aug 27 '12 at 16:40
up vote 3 down vote accepted

In general, differentiability is the property of having a derivative. The difference is the same as that between the inverse and invertibility.

share|cite|improve this answer
the question should be of course: What is the difference between Complex derivative and Complex differentiable? – alvoutila Aug 27 '12 at 19:07
@alvoutila: Apart from the apparent linguistic difference, there is nothing else. Complex derivative exists for a function if and only if it is complex differentiable. – timur Aug 27 '12 at 19:16

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.