Question:
Find $\frac{\mathrm{dy}}{\mathrm{dx}}$, when
$x=a t^{2}$ and $y=2 a t$
Solution:
Given that $x=a t^{2}, y=2 a t$
So, $\frac{\mathrm{dx}}{\mathrm{dt}}=\frac{\mathrm{d}\left(\mathrm{at}^{2}\right)}{\mathrm{dt}}=2 \mathrm{at}$
$\frac{\mathrm{dy}}{\mathrm{dt}}=\frac{\mathrm{d}(2 \mathrm{at})}{\mathrm{dt}}=2 \mathrm{a}$
Therefore, $\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{2 a}{2 a t}=\frac{1}{t}$
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