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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.
geometrically, the function #f# is differentiable at #a# if it has a non-vertical tangent at the corresponding point on the graph, that is, at #(a,f(a))#. That means that the limit. #lim_{x\to a} (f(x)-f(a))/(x-a)# exists (i.e, is a finite number, which is the slope of this tangent line). When this limit exist, it is called derivative of #f# at #a# and denoted #f'(a)# or #(df)/dx (a)#.