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If x^(2) y^(5) = (x + y)^(7) , " then " ...

If `x^(2) y^(5) = (x + y)^(7) , " then " (d^(2)y)/(dx^(2))` is equal to

A

`y//x^(2)`

B

`x//y`

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Given , ` x^(2) y^(5) = (x + y)^(7)`
Taking log on both sides , we get
` 2 log x + 5 log y = 7 log (x + y)`
On differentiating both sides w.r.t.x, we get
`(2)/(x) + (5)/(y) (dy)/(dx) = (7) /(x + y) (1 + (dy)/(dx)) `
`rArr (dy)/(dx) ((7)/(x + y) - (5)/(y)) = (2)/(x) - (7)/(x +y)`
` rArr (dy)/(dx) = (y)/(x)`
Again , differentiating both sides w.r.t.x, we get
`(d^(2) y)/(dx^(2)) = (x(dy)/(dx) - y)/(x^(2))`
` = (x . (y//x)-y)/(x^(2))" "` [from Eq.(i)]
= 0
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MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-DIFFERENTIATION -MHT CET CORER
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