Question

If $x=\psi \left(t\right)andy=\psi \left(t\right)$, then $\frac{d^{2}y}{d{x}^2}$ is equal to (dashes denote the derivative w.r.t ‘t’)

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$\frac{dy}{dx}=\frac{{\psi }^{\prime }}{{\Phi }^{\prime }}\frac{d^{2}y}{d{x}^2}=\frac{d}{dx}\left(\frac{dy}{dx}\right)=\frac{\frac{d}{dt}\left(\frac{dy}{dx}\right)}{\frac{dx}{dt}}=\frac{\frac{{\Phi }^{\prime }{\psi }^{\prime \prime }-{\psi }^{\prime }{\Phi }^{\prime \prime }}{({\Phi }^{\prime }{)}^{\prime }}}{{\Phi }^{\prime }}$