Question

I am confused re: the chapter "derivative of an inverse function". How can the derivative of f^-1(x) be 1/the derivative of f(x)? Just looking at an example: the derivative of e^x is e^x... but the derivative of ln(x) sure as hell isn't 1/e^x.

Answer 1

the derivative of f^-1(x) is 1/the derivative of the inverse function, d{f -1(x)}/dx = 1 f '(f -1(x))

Answer 2

sorry i was wrong the derivative f^-1(x) is 1/the derivative of the function evaluated at the inverse. So in your case it's 1/(e^ln(x)).