Differentiating in Polar Form

Defining polar coordinates and differentiating in polar form.

Mapped to AP College Board # FUN-3, FUN-3.G, FUN-3.G.1, FUN-3.G.2

Recognizing opportunities to apply derivative rules can simplify differentiation. Calculate derivatives of functions written in polar coordinates. Methods for calculating derivatives of realvalued functions can be extended to functions in polar coordinates. For a curve given by a polar equation r = f(θ), derivatives of r, x, and y with respect to θ, and first and second derivatives of y with respect to x can provide information about the curve.