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If x=varphi(t), y=psi(t),t h e n(d^(2y))...

If `x=varphi(t), y=psi(t),t h e n(d^(2y))/(dx^2)` is `(varphi^(prime)psi^-psi'varphi' ')/((varphi^(prime))^2)` (b) `(varphi^(prime)psi^-psi'varphi' ')/((varphi^(prime))^3)` `varphi^(/)psi^` (d) `psi^(/)varphi^`

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

`"We have "x=phi(t),y=psi(t)." Therefore,"`
`(dy)/(dx)=((dy)/(dt))/((dx)/(dt))=(psi')/(phi')`
`"or "(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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