For a curve defined parametrically by and

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

Problem

For a curve defined parametrically by

x=f(t)

and

y=g(t)

, where

\dfrac{dx}{dt}\neq 0

, which of the following expressions equals

\dfrac{dy}{dx}

expressed in terms of derivatives with respect to

t

? (a)

(dy/dt)\,(dx/dt)

(b)

\dfrac{dy/dt}{dx/dt}

(c)

\dfrac{dx/dt}{dy/dt}

(d)

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