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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
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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

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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.

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the question should be of course: What is the difference between Complex derivative and Complex differentiable? –  laovultai 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

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