Step 1

Given : The sides of the two squares are $x$ and $y$ and

$ y = x-x^2$

Area of the I square is $ x^2$

Area of the II square is $ y^2$

$=(x-x^2)^2$

Let $A_1=x^2$

Differentiating w.r.t $x$ we get

$ \large\frac{dA_1}{dx}=2x$

$ A_2=(x-x^2)^2$

Differentiating w.r.t $x$ we get

$ \large\frac{dA_2}{dx}=2(x-x^2)(1-2x)$

$ =4x^3-6x^2+2x$

$=2x(2x^2-3x+1)$

$\large\frac{dA_1}{dx} (2x^2-3x+1)$

Hence rate of change in area w.r.t the area of the first square is

$ 2x^2-3x+1$