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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.
As a result, the graph of a differentiable function must have a (non-vertical) tangent line at each point in its domain, be relatively smooth, and cannot contain any breaks, bends, or cusps. More generally, if x0 is a point in the domain of a function f, then f is said to be differentiable at x0 if the derivative f â²(x0) exists. This means that the graph of f has a non-vertical tangent line at the point (x0, f(x0)).