Question
If $x=a t^2, y=2 a t$, then find $\frac{d y}{d x}$
We have, $y=2 a t$
$\frac{d y}{d t}=2 a \frac{d}{d t}(t)=2 a(1)=2 a$
also $x=a t^2$
$\frac{d x}{d x}=a \frac{d}{d t}\left(t^2\right)=a(2 t)=2 a t$
now $\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{2 a}{2 a t}=\frac{1}{t}$
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