Find dy dx in the following cases: xy = c^2 - Vidyadip

Question

Find $\frac{\text{dy}}{\text{dx}}$ in the following cases: $xy = c^2$

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Answer

We have, $xy = c^2$
Differentiating with respect to $x,$ we get
$\frac{\text{d}}{\text{dx}}(\text{xy})=\frac{\text{d}}{\text{dx}}(\text{c}^2)$
$\Rightarrow\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}\frac{\text{d}}{\text{dx}}(\text{x})=0$
$[$Using product rule$]$
$\Rightarrow\text{x}\frac{\text{dy}}{\text{dx}}+\text{y}=0$
$\Rightarrow\text{x}\frac{\text{dy}}{\text{dx}}=-\text{y}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=-\frac{\text{y}}{\text{x}}$

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