### Home > CALC > Chapter 6 > Lesson 6.4.2 > Problem 6-149

6-149.

*e*^{ln}* ^{x}* =

*x*is another way of saying that

*y*=

*e*and

^{x}*y*= ln

*x*are inverse functions.

Inverse functions have reciprocal derivatives at their corresponding (

*x*,

*y*) → (

*y*,

*x*) values.

If *f*(*x*) has coordinate point (*a*, *b*).

And if *g*(*x*) is the inverse of *f*(*x*),

Let *f*(*x*) = *e ^{x}* and

*g*(

*x*) = ln

*x*.

First find

*f*'(

*x*) = _____. (This should be easy!)

To find *g*'(*x*), take the reciprocal of *f* '(*x*), but NOT at the

*x*-value...

Now evaluate *g*'(*x*) when *f*(*x*) = *e ^{x}*.