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

Answer: (C)

We have,
$y=\frac{c}{t}$
$\Rightarrow \frac{dy}{dt}=\frac{-c}{t^2}$
Also, $x=ct$
$\Rightarrow \frac{dx}{dt}=c$
$\therefore \frac{dy}{dx}=\frac{(dy/dt)}{(dx/dt)}=\frac{\frac{-c}{t^2}}{c}=\frac{-1}{t^2}$
On putting $t=2$, we get
$\frac{dy}{dx}=-\frac{1}{4}$