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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.
The function f is said to be of (differentiability) class Ck if the derivatives fâ², fâ²â², ..., f(k) exist and are continuous (the continuity is implied by differentiability for all the derivatives except for f(k)). The function f is said to be of class Câ, or smooth, if it has derivatives of all orders.