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

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