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(d^2x)/(d y^2) equals...

`(d^2x)/(d y^2)` equals

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)`
`(d^(2) x)/(dy^(2)) = - ((d^(2) x)/(dy^(2)))((dy)/(dx))^(-2) ((dx)/(dy))`
` = - ((d^(2) x)/(dy^(2)))((dy)/(dx))^(-3)` .
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