1. 5.4 Exponential Functions: Differentiation and Integration The inverse of f(x) = ln x is f -1 = e x. Therefore, ln (e x ) = x and e ln x = x Solve for x in the following equations. Take the ln of both sides.

2. Operations with Exponential Functions The Derivative of the Natural Exponential Function Differentiate.

3. Find the relative extrema of Since e x never = 0, -1 is the only critical number. neg. dec. pos. inc. Therefore, x = -1 is a min. by the first derivative test. Minimum @ ?

4. Integration Rules for Exponential Functions Ex. Let u = 3x + 1 du = 3 dx

5. Ex. Let u = -x 2 du = -2x dx Ex. Let u = 1/x = x -1

6. Ex. Let u = cos x du = -sin x dx Ex. Let u = -x du = -dx -du = dx

7. Ex. Let u = e x du = e x dx