Q. 115.0( 1 Vote )

# x and y are the s

Answer :

Given: two squares of sides x and y, such that y = x-x2

To find: the rate of change of the area of the second square with respect to the area of the first square

Explanation: Let the area of the first and the second square be A1 and A2 respectively.

Then Area of the first square is

A1 = x2

Differentiating this with respect to time, we get  And the area of the second square is

A2 = y2…….(ii)

But given, y = x-x2

Substituting this given value in equation (ii), we get

A2 = (x-x2)2 …….(iii)

Now differentiating equation (iii) with respect to t, we get Now applying the power rule of differentiation, we get Now applying the sum rule of differentiation, we get Applying the derivative, we get   We need to find the rate of change of area of the second square with respect to the area of the first square, i.e., Substituting values from equation (i) and (iv), we get By cancelling the like terms we get    Hence the rate of change of the area of the second square with respect to the area of the first square is 2x2-3x+1

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