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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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    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 $\mathbb{R}$.2012-08-27

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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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    @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.2012-08-27