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(d^2x)/(dy^2) equals: (1) ((d^2y)/(dx^2...

`(d^2x)/(dy^2)` equals: (1) `((d^2y)/(dx^2))^(-1)` (2) `-((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-3)` (3) `((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-2)` (4) `-((d^2y)/(dx^2))^(-1)((dy)/(dx))^(-3)`

A

`((d^(2)y)/(dx^(2)))^(-1)`

B

`-((d^(2)y)/(dx^(2)))^(-1)((dy)/(dx))^(-3)`

C

`((d^(2)y)/(dx^(2)))((dy)/(dx))^(-2)`

D

`-((d^(2)y)/(dx^(2)))((dy)/(dx))^(-3)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, `(dx)/(dy) = 1/(dy//dx) = ((dy)/(dx))^(-1) `
` rArr" " d/(dy) ((dx)/(dy)) = d/(dx) ((dy)/(dx))^(-1) (dx)/(dy) `
` rArr" " (d^(2)x)/(dy^(2)) =- ((d^(2)y)/(dx^(2)))((dy)/(dx))^(-2)((dx)/(dy)) =- ((d^(2)y)/(dx^(2))((dy)/(dx))^(-3) `
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