Let g be the inverse of a function satisfying '(x) = '(x). Show that g'(x) =

Let g be the inverse of a function ƒ satisfying ƒ'(x) = ƒ'(x). Show that g'(x) = x⁻¹. This shows that the inverse of the exponential function ƒ(x) = e^x is an antiderivative of x⁻¹. That inverse is the natural logarithm function that we define in the next section.