Let (x) = x n and g(x) = x 1 . Compute g'(x) using Theorem 2 and check your answer using the Power Rule. THEOREM

Let ƒ(x) = xⁿ and g(x) = x¹. Compute g'(x) using Theorem 2 and check your answer using the Power Rule.

THEOREM 2 Derivative of the Inverse Assume that f is differentiable and one-to- one with inverse g(x) = f(x). If b belongs to the domain of g and f'(g(b)) #0, then g'(b) exists and g' (b) = 1 f'(g(b)) 3