Question

If $x=ct$ and $y=\frac{c}{t}$, find $\frac{dy}{dx}$ at $t=2$

• A. $\frac{1}{4}$
• B. $4$
• C. $-\frac{1}{4}$
• D. $0$

Answer 1

The correct option is C $-\frac{1}{4}$

We have, $x=ct\Rightarrow \frac{dx}{dt}=c$

and $y=\frac{c}{t}\Rightarrow \frac{dy}{dt}=-\frac{c}{t^2}$

$\therefore \frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=-\frac{1}{t^2}$

Hence at $t=2$

$\frac{dy}{dx}=-\frac{1}{2^2}=-\frac{1}{4}$