# What is the difference between Complex derivative and Complex differentiability?

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?

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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

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

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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