`xa n dy` are the sides of two squares such that `y=x-x^2` . Find the rate of the change of the area of the second square with respect to the first square.

Explanation

Since, x and y are the sides of two squares such that y`=x-x^(2)`
`therefore` Area of the first square `(A_(1))=x^(2)`
and area of the second square `(A_(2)) = y^(2)=2(x-x^(2))((dx)/(dt)-2x.(dx)/(dt))`
`=(dx)/(dt)(1-2x)2(x-x^(2))`
and `(dA_(1))/(dt) = d/(dt)(x^(2)) = 2x.(dx)/(dt)`
`therefore (dA_(2))/(dA_(1)) = (dA_(2)//dt)/(dA_(1)//dt) = ((dx)/(dt).(1-2x)(2x-2x^(2)))/(2x.(dx)/(dt))`
`=(1-2x)(1-x)`
`=1-x-2x+2x^(2)`
`=2x^(2) - 3x+1`