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