Find d y d x if : x=a t^4, y=2 a t^2 - Vidyadip

Question

Find $\frac{d y}{d x}$ if : $x=a t^4, y=2 a t^2$

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Answer

Given, $y=2 a t^2$
Differentiate w.r.t.t
$
\frac{d y}{d t}=2 a \frac{d}{d t}\left(t^2\right)=2 a(2 t)=4 a t . \ldots
$
And, $x=a t^4$
Differentiate w.r.t.t
$
\frac{d x}{d t}=a \frac{d}{d t}\left(t^4\right)=a\left(4 t^3\right)=4 a t^3 \ldots .
$
Now, $\frac{d y}{d x}=\frac{\frac{d y}{d t}}{\frac{d x}{d t}}=\frac{4 a t}{4 a t^3} \ldots[$ From (I) and (II) $]$
$
\therefore \quad \frac{d y}{d x}=\frac{1}{t^2}
$

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