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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.
Formally, a function of several real variables f: R â R is said to be differentiable at a point x0 if there exists a linear map J: R â R such that. If a function is differentiable at x0, then all of the partial derivatives must exist at x0, in which case the linear map J is given by the Jacobian matrix.