Find d y d x if x =5 t ^2, y =10 t - Vidyadip

Question

Find $\frac{d y}{d x}$ if $x =5 t ^2, y =10 t$

✓

Answer

$
x=5 t^2, y=10 t
$
Differentiating $x$ and $y$ w.r.t. $t$, we get
$
\begin{aligned}
& \frac{d x}{d t}=5 \frac{d}{d t}\left(t^2\right)=5 \times 2 t=10 t \\
& \text { and } \frac{d y}{d t}=10 \frac{d}{d t}(t)=10 \times 1=10 \\
& \therefore \frac{d y}{d x}=\frac{(d y / d t)}{(d x / d t)}=\frac{10}{10 t}=\frac{1}{t}.
\end{aligned}
$

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