# Derivative of Natural Log Function

- Author:
- Tim Brzezinski

- Topic:
- Derivative, Function Graph, Logarithm

Displayed below is a graph of the function .
Drag the

**BIG WHITE POINT**along the graph of this function to**trace out the graph of the derivative of this function.**Does this function look familiar? Interact with this applet for a minute, then answer the question that follows.## 1.

Why is the derivative of the function never negative? Explain how you know.

## 2.

Rewrite the equation in exponential form.

## 3.

Use implicit differentiation to differentiate both sides of this equation (you wrote in your response for (2)) with respect to *x*. Then solve for *y*. What do you get?

## 4.

Rewrite solely in terms of *x*.