Solve the below:
Q: Let f(x)={(x^3)cos(1/x) if xâ? 0, 0 if x=0,
and
g(x)={(1/x)sin(x) if xâ? 0, 0 if x=0.
a) Using the definition of the derivative show that f is differentiable at 0 and determine f '(0).
b) Is g differentiable at 0? Justify your answer.
c) Show that f ' ^(x) and g ' ^(x) exist for xâ? 0 and determine their values.