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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)((dx)/(dy))^(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)))((dy)/(dx))^(-3)`

B

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

C

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

D

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

Text Solution

Verified by Experts

We have
`(d^(2)x)/(dy^(2))=(d)/(dy)=((dx)/(dy))=(d)/(dy)(((1)/(dy))/(dx))cdot(dx)/(dy)`
`=-(1)/(((dy)/(dx))^(2))cdot(d^(2)y)/(dx^(2))cdot(1)/(((dy)/(dx)))`
`=-(1)/(((dy)/(dx))^(3))cdot(d^(2)y)/(dx^(2))`
`=-((dy)/(dx))^(-3)((d^(2)y)/(dx^(2)))`
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