Answer
$\frac{dA}{ds} = 12$ $cm$
Work Step by Step
The exercise is asking for the rate of change for area $A$ with respect to its sides $s$. Therefore, it's simply asking us for the first derivative of the function $A$: $$A=s^{2}$$ $$(\frac{d}{ds})A = s^{2} (\frac{d}{ds})$$ $$\frac{dA}{ds} = 2s^{2-1} = 2s$$. For the value $s = 6cm$: $$\frac{dA}{ds} = 2(6) = 12 cm$$
