Chapter 4: Applications of Differential Calculus

 To find the slope of a polar curve r=f(Θ), express it in parametric form of x=f(Θ)cosΘ and y=f(Θ)sinΘ.

dx/dΘ= f'(Θ)cosΘ- f(Θ)sinΘ and dy/dx= f'(Θ)sinΘ+ f(Θ)cosΘ

Therefore, dy/dx= (dy/dΘ)/(dx/dΘ)= [f'(Θ)sinΘ+ f(Θ)cosΘ]/[f'(Θ)cosΘ- f(Θ)sinΘ]

If this equation is at all unclear, it is also written out in the example and in the Barron's book, page 190.