Question

Find $\frac{dy}{dx}$, when

$x=a{t}^2\mathrm{and}y=2at$

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have},x=a{t}^2\mathrm{and}y=2at \\ \Rightarrow \frac{dx}{dt}=2at\mathrm{and}\frac{dy}{dt}=2a \\ \therefore \frac{dy}{dx}=\frac{{\displaystyle \frac{dy}{dt}}}{{\displaystyle \frac{dx}{dt}}}=\frac{2a}{2at}=\frac{1}{t} \end{gathered}$$