Exponential function gradient

The gradient of an exponential graph at any point is directly proportional to the value of the function at that point (or the coordinate of the graph).

This can be written as:

Gradient of

The graph of has an interesting property - its gradient at any point is identical to the coordinate of that point.

For example, at , the point on the graph is . The gradient at this point is also .

This can be written as:

Reminder: this ONLY works for base . Other bases will have different gradients to their values.

Gradient of

When we have an exponential function with a coefficient in the exponent, i.e. , the gradient is proportional to both the value of the function and the coefficient .

We can write this as:

For example, for the function , the gradient at any point is 3 times the value at that point.