We differentiate polar functions.

The previous section discussed a special class of parametric functions called polar functions. We know that and so we can compute the derivative of with respect to using differentials: provided that . With polar functions we have so provided that .

When the graph of the polar function intersects the origin (sometimes called the “pole”), then for some angle .

When , what is the formula for ?
. . .
The answer to the question above leads us to an interesting point. It tells us the slope of the tangent line at the pole. When a polar graph touches the pole at , the equation of the tangent line in polar coordinates at the pole is .