Question

If $x=5t^4$ and $y=2t^2+1,$ then $\frac{dy}{dx}$ at $t=1$ is equal to

[2 marks]

• A. $\frac{1}{5}$
• B. $5$
• C. $\frac{1}{3}$
• D. $3$

Answer 1

The correct option is A $\frac{1}{5}$

We have, $x=5t^4$
$\Rightarrow \frac{dx}{dt}=20t^3$
and, $y=2t^2+1$
$\Rightarrow \frac{dy}{dt}=4t$
$\therefore \frac{dy}{dx}=\frac{dy/dt}{dx/dt}$
$\Rightarrow \frac{dy}{dx}=\frac{4t}{20t^3}=\frac{1}{5t^2}$
At $t=1,$ $\frac{dy}{dx}=\frac{1}{5}$