Definition of Differentiable function

Let f be a function with domain D in R, the real numbers, and D is an open set in R. Then the derivative of f at the point c is defined as: f'(c) =lim as x-> c of the difference quotient [f(x)-f(c)]/[x-c] If that limit exits, the function is called differentiable at c. If f is differentiable at every point in D then f is called differentiable in D.