For differentiable parametric equations and with

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For differentiable parametric equations

x=f(t)

and

y=g(t)

with

\frac{dx}{dt}\neq 0

, which of the following expressions gives

\dfrac{d^{2}y}{dx^{2}}

? (a)

\displaystyle \frac{d}{dx}\left(\frac{dy}{dt}\right)

(b)

\displaystyle \frac{\dfrac{d^{2}y}{dt^{2}}}{\dfrac{d^{2}x}{dt^{2}}}

(c)

\displaystyle \frac{d}{dt}\left(\frac{dy}{dx}\right)\,\Big/\,\frac{dx}{dt}

(d)

\displaystyle \frac{\dfrac{d^{2}y}{dt^{2}}}{\dfrac{dx}{dt}}