1. **State the problem:** Find the derivative of the function $$r = \sin(0^2) \cos(20)$$ with respect to the variable (assumed as $x$). 2. **Simplify the function:** Since $0^2 = 0$, $$r = \sin(0) \cos(20).$$ 3. **Evaluate constants:** $$\sin(0) = 0,$$ so $$r = 0 \cdot \cos(20) = 0.$$ The function $r$ is a constant zero. 4. **Find the derivative:** The derivative of a constant is zero, so $$\frac{dr}{dx} = 0.$$