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if y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/(sq...

if `y=((a-x)sqrt(a-x)-(b-x)sqrt(x-b))/(sqrt(a-x)+sqrt(x-b))` then `dy/dx` wherever it is defined is equal to`:`

A

`(x+(a+b))/(sqrt((a-x)(x-b)))`

B

`(2x-a-b)/(2sqrt(a-x)sqrt(x-b))`

C

`-((a+b))/(2sqrt((a-x)(x-b)))`

D

`(2x+(a+b))/(2sqrt((a-x)(x-b)))`

Text Solution

Verified by Experts

The correct Answer is:
B
`y=((a-x)^(3//2)+(x-b)^(3//2))/(sqrt(a-x)+sqrt(x-b))`
`=((sqrt(a-x)+sqrt(x-b))(a-x-sqrt(a-x)sqrt(x-b)+x-b))/(sqrt(a-x)+sqrt(x-b))`
`=a-b-sqrt(a-x)sqrt(x-b)`
`therefore" "(dy)/(dx)=(1)/(2sqrt(a-x))sqrt(x-b)-(1)/(2sqrt(x-b))sqrt(a-x)`
`=(2x-a-b)/(2sqrt(a-x)sqrt(x-b))`
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