Chapter 12.5, Problem 69E

To determine

To prove: That the curvature k for the polar equation at the point $\left(r,\theta \right)$ is

$k=\frac{\left|2{\left(r^{\prime }\right)}^2-r.r^{″}+r^2\right|}{{\left[{\left(r^{\prime }\right)}^2+r^2\right]}^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$.