Question

Find $\frac{dy}{dx}$ if $x=2a{t}^2,y=a{t}^3$

Answer 1

$x=2a{t}^2$

$\frac{dx}{dt}=2a\left(2t\right)=4at$

$y=a{t}^3$

$\frac{dy}{dt}=a\left(3t^2\right)=3a{t}^2$

$\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}=\frac{3a{t}^2}{4at}=\frac{3t}{4}$

$\therefore \frac{dy}{dx}=\frac{3t}{4}$