## Thomas' Calculus 13th Edition

$r'=\frac{-θsinθ}{(cosθ)^{1/2}}+2(cosθ)^{1/2}$
Rewrite the equation: $r=2θ(cosθ)^{1/2}$ Take the derivative of the equation using Trigonometric derivatives, Product Rule, and Chain Rule: $r'=2θ\times\frac{1}{2}(cosθ)^{-1/2}\times-sinθ+2(cosθ)^{1/2}$ $=\frac{-θsinθ}{(cosθ)^{1/2}}+2(cosθ)^{1/2}$