# in the above question i m geting ans D but the ans js B plz expalin me

Susmita
425 Points
3 years ago
Given  $x=\phi (t)$ and $y=\psi (t)$
Differentiate with respect  to t.
$\frac{dx}{dt} = \phi ' (t)$ and $\frac{dy}{dt} = \psi ' (t)$
Now $\frac{dy}{dx} = \frac{dy}{dt} \frac{dt}{dx} =\frac{\psi '}{\phi '}$
$\frac{d^2 y}{dx^2} =\frac{d}{dx}( \frac{dy}{dx})$
$=\frac{d}{dt} (\frac{dy}{dx} ) \frac{dt}{dx}$
$=\frac{d}{dt} (\frac{\psi '}{\phi '} ) \frac{1}{\phi '}$
$=(\frac{\phi ' \psi '' - \psi ' \phi ''}{\phi '^2} ) \frac{1}{\phi '}$
So the ans is b.Please approve the answer if you are helped.