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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.
Historical Examples. 1  The most important theorem in regard to differentiable functions is the âtheorem of intermediate value.â. 2  Particular interest attaches to continuous functions which are not differentiable. 3  Accordingly the function is not differentiable at any point. Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 3 Various. If the function of x is differentiable, the differential Partial differentiation. Encyclopaedia Britannica, 11th Edition, Volume 14, Slice 5 Various.