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If x = t^(2) and y = t^(3), then (d^(2)y...

If `x = t^(2)` and `y = t^(3)`, then `(d^(2)y)/(dx^(2))` is equal to

A

`3/2`

B

`3/(4t)`

C

`3/(2t)`

D

`(3)/(2t)`

Text Solution

Verified by Experts

The correct Answer is:
B
We have, `x = t^(2)` and `y = t^(3)`
`:. (dx)/(dt) =2t` and `(dy)/(dt) = 3t^(3)`
`:. (dy)/(dx) = (dy//dt)/(dx.//dt) = (3t^(2))/(2t) = 3/2 t`
On further differentiating w.r.t.x, we get
`(d^(2)y)/(dx^(2)) = 3/2.(d)/(dt)t.(dt)/(dx)`
`= 3/2.(1)/(2t), [:' (dt)/(dx) = 1/(2t)]`
`= (3)/(4t)`
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