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If x=phi(t),y=Psi(t)," then "(d^(2)y)/(d...

If `x=phi(t),y=Psi(t)," then "(d^(2)y)/(dx^(2))` is equal to

A

`(phi'Psi''-Psi'phi'')/((phi')^(2))`

B

`(phi'Psi''-Psi'phi'')/((phi')^(3))`

C

`(phi'')/(Psi'')`

D

`(Psi'')/(phi'')`

Text Solution

Verified by Experts

The correct Answer is:
B
We have , ` x = phi (t) , y= Psi(t)`
`therefore (dy)/(dx) = (dy//dt)/(dx//dt) = (Psi')/(phi')`
` rArr (d^(2) y)/(dx^(2)) = (d)/(dx) ((Psi')/(phi'))= (d)/(dt) ((Psi')/(phi')) (dt)/(dx) `
` = (phi'Psi''-Psi'phi'')/((phi')^(2)).(1)/(phi') = (phi'Psi''- Psi'phi'')/((phi')^(3))` .
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