For the parametric curve defined by and

MATHEMATICS · Single correct · AP · Calculus BC · Parametric, Polar, and Vector-Valued Functions · Parametric, Polar, and Vector-Valued Functions

Problem

For the parametric curve defined by

x=t^{2}

and

y=\sin t

, which of the following notations correctly denotes the second derivative of

y

with respect to

x

? (a)

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

(b)

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

(c)

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

(d)

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