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In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.
exists for every c in (a, b). Basically, f is differentiable at c if f'(c) is defined, by the above definition. Another point of note is that if f is differentiable at c, then f is continuous at c. Let's go through a few examples and discuss their differentiability. First, consider the following function.