Mathematics

Problem

For differentiable functions

x(t)

and

y(t)

with

\dfrac{dx}{dt}\neq 0

, which of the following expressions is equal to

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

? a)

\displaystyle \frac{\left(\dfrac{dy}{dt}\right)\left(\dfrac{d^{2}x}{dt^{2}}\right)}{\left(\dfrac{dx}{dt}\right)^{3}}

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

\displaystyle \frac{\dfrac{d^{2}y}{dt^{2}}}{\left(\dfrac{dx}{dt}\right)^{2}}

\displaystyle \frac{\dfrac{d}{dt}\!\left(\dfrac{dy}{dx}\right)}{\dfrac{d^{2}x}{dt^{2}}}