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Q.

If y=(a−x)a−x−(b−x)x−ba−x+x−b then dydx whenever it is defined is

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a

x+(a+b)(a−x)(x−b)

b

2x−a−b2a−xx−b

c

−(a+b)2(x−x)(x−b)

d

2x+(a+b)2(a−x)(x−b)

answer is B.

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Detailed Solution

y=(a−x)3/2+(x−b)3/2a−x+x−b=(a−x+x−b)(a−x−a−xx−b+x−b)a−x+x−b=a−b−a−xx−bdydx=12a−xx−b−12x−ba−x=2x−a−b2a−xx−b
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If y=(a−x)a−x−(b−x)x−ba−x+x−b then dydx whenever it is defined is