# Task 4: Gradient function of natural log

- Author:
- qehsmaths

Explore the gradient function of natural log ( ) by considering the connection between the exponential function and the natural log function.
The graphs displayed are , , and . In addition, point P on and point Q on are shown. Tangents are shown at these points and the gradients of the tangents are displayed.

1. What transformation maps the graph to the graph ?
Adjust the point P using the slider for p.
2. At any point on the graph, if the gradient of y=e^x is m, what is the gradient of y=ln(x)?
( .
(At the point , the gradient of is .
So at the point , the gradient of is ...
So at the point , the gradient of is ...

*Hint*: think about the dimensions of the triangles.) 3. Work out the gradient function for