> Under who's definition W. Rudin, Principles of Mathematical Analysis. W. Fleming, Functions of Several Variables. For the set of real numbers R, a function

> Under who's definition W. Rudin, Principles of Mathematical Analysis. W. Fleming, Functions of Several Variables. For the set of real numbers R, a function f: R --> R x in R, d in R, function f is differentiable at x with value d provided for h in R lim_{h --> 0} (f(x + h) - f(x))/h = d In this case we write f'(x) = df(x)/dx = d In that case, in particular, lim_{h --> 0} (f(x + h) - f(x)) = 0 so that f is continuous at x. Differentiation is important in physics, e.g., in Newton's second law.