For a smooth curve defined parametrically by and where

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

Problem

For a smooth curve defined parametrically by

x = x(t)

and

y = y(t)

where

\dfrac{dx}{dt}\neq 0

, which of the following expressions gives the slope

\dfrac{dy}{dx}

at the parameter value

t

? (a)

\displaystyle \frac{dy}{dt}\,\frac{dx}{dt}

(b)

\displaystyle \frac{d}{dt}\left(\frac{y}{x}\right)

(c)

\displaystyle \frac{dy}{dt}\Big/\frac{dx}{dt}

(d)

\displaystyle \frac{dx}{dt}\Big/\frac{dy}{dt}