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