Exponential graph gradient

An important property of an exponential graph is that the *gradient8 of it is directly proportional to the value of at that point.

That means that, for a function in the form , we can write the gradient as (where is a constant of proportionality).

In other words, the gradient of the graph is the coordinate multiplied by something.

Gradient of

There’s a special case of this when the base is . The gradient at any point is exactly the same as the value at that point.

We’ll learn more about that in the base e exponentials topic, but for now, just remember that the gradient of is itself.