x and y are the sides of two square such that `y=x-x^(2)`. The rate of change of area of the second square with respect to that of the first square is

Options

A. `2x^(2)+3x+1`
B. `2x^(2)+2x-1`
C. `2x^(2)-3x+1`
D. `3x^(2)+2x+1`

Answer

C

Explanation

Let area of first square `A=x^(2)` and area of second square `B=y^(2)=(x-x^(2))^(2) [ :' y=x-x^(2)` given `]`
`:.(dB)/(dA)=((dB)/(dx))/((dA)/(dx))=(2(x-x^(2))(1-2x))/(2x)`
`=(1-x)(1-2x)=2x^(2)-3x+1`