Question

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

Answer 1

Given: $x=a{t}^2,y=2at$
Finding $\frac{dy}{dt}$
$y=2at$
$\frac{dy}{dt}=\frac{d\left(2at\right)}{dt}=2a$
Finding $\frac{dx}{dt}$
$x=a{t}^2$
$\frac{dx}{at}=\frac{d\left(a{t}^2\right)}{dt}=2at$
Now, $\frac{dy}{dx}=\frac{\frac{dy}{dt}}{\frac{dx}{dt}}$ ...(i)
Now, substituting the value of $\frac{dy}{dt}$ and $\frac{dx}{dt}$ in (i), we get
$\frac{dy}{dx}=\frac{2a}{2at}=\frac{1}{t}$