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If x=at^2,y=at,then (d^2y)/(dx^2)=...

If `x=at^2`,`y=at`,then `(d^2y)/(dx^2)=`

A

`-(1)/(t^2)`

B

`(1)/(2at^3)`

C

`-(1)/(t^3)`

D

`-(1)/(2at^3)`

Text Solution

Verified by Experts

The correct Answer is:
D
`(dy)/(dx)=((dy)/(dt))/((dx)/(dt))=(2a)/(at)implies(dy)/(dx)=(1)/(t)=(2a)/(y)`
`impliesy(dy)/(dx)=2aimpliesy(d^(2)y)/(dx^(2))+((dy)/(dx))^(2)=0`
`implies(d^(2)y)/(dx^(2))=(-((dy)/(dx))^(2))/(y)=-(1)/(2at^(3))`
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