Suppose and are differentiable functions of time linked by

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

Suppose

x

and

y

are differentiable functions of time

t

linked by

x^{2}y=10

. If

\dfrac{dx}{dt}

is known, which expression gives

\dfrac{dy}{dt}

in terms of

x

y

, and

\dfrac{dx}{dt}

? (a)

\displaystyle \frac{dy}{dt}=\frac{2y}{x}\,\frac{dx}{dt}

(b)

\displaystyle \frac{dy}{dt}= -\frac{2y}{x}\,\frac{dx}{dt}

(c)

\displaystyle \frac{dy}{dt}= -\frac{2x}{y}\,\frac{dx}{dt}

(d)

\displaystyle \frac{dy}{dt}= -\frac{y}{x}\,\frac{dx}{dt}