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If sqrt(y-x)+sqrt(y+x)=1" then "(d^(3)y)...

If `sqrt(y-x)+sqrt(y+x)=1" then "(d^(3)y)/(dx^(3))` at x=1 is equal to

A

2

B

1

C

0

D

Does bot exist

Text Solution

Verified by Experts

The correct Answer is:
A
`sqrt(y-x)+sqrt(y+x)=1`
`y-x+y+x+2sqrt(y^(2)-x^(2))=1`
`(2y-1)=-2sqrt(y^(2)-x^(2))`
`4y^(2)-4y+1=4y^(2)-4x^(2)" (squaring on both sides)"`
`4x^(2)-4y+1=0`
`8x-4(dy)/(dx)=0rArr" "(dy)/(dx)=2`
`"So, "(d^(2)y)/(dx)=2rArr(d^(3)y)/(dx^(3))=3`.
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