Consider the two functions with f(0) = g(0) = 0 and otherwise f(x) = sin(x)[sin( 1 x ) 1] and g(x) = [cos(x) 1] cos( 1 x ). One is differentiable at 0. The other is not.

(a) Use the definition of the derivative to determine which is differentiable and find its derivative at 0.

(b) Show that the other is not differentiable at 0