Let (u) = u q and g(x) = x p/q . Assume that g is differentiable. (a)

Let ƒ(u) = u^q and g(x) = x^p/q. Assume that g is differentiable.
(a) Show that ƒ(g(x)) = x^p (recall the Laws of Exponents).
(b) Apply the Chain Rule and the Power Rule for whole-number exponents to show that ƒ'(g(x)) g'(x) = px^p−1.
(c) Then derive the Power Rule for x^p/q.