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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)/(psi')`
`Rightarrow (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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