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What is a differentiability?

What is a differentiability? Here are some definitions.

Noun
  1. The ability to be differentiated.
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Examples
This module is an exercise on the continuity and differentiability of real functions.
The book then returns to foundations with chapters on contiguity and L2 differentiability.
Also, we consider the concept of general differentiability for fuzzy functions and we plot the h-curve to illustrate the region of convergence in different levels.
These functions are most widely used because of their easy differentiability but other variants are also possible.
Because of the demands of differentiability in distribution theory, the spaces of test-functions and their duals are somewhat more complicated.
For example, the important distinctions between continuity and differentiability and between uniform and pointwise continuity seem to have no basis in intuition.

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