## Differentiating Linear Functions

Here, we will find the derivative of the function Of course, the graph of this function is a line through the origin with slope one.

As for constant functions, the tangent line to the graph is the same line. Since the derivative measures the slope of the tangent line, we expect the following:

Derivative of the identity function

Again, we can see this by computing the average change of the function. If we start with a point and compute the rate of change to some other point we see that

Since the average rate of change is always one, when we consider very small values of , we obtain as we expected.