Question

Find \[\frac{dy}{dx}\] in the following case \[xy = c^2\]  ?

Answer 1

\[\text{We have, xy } = c^2 \]

Differentiating with respect to x, we get,

\[\frac{d}{dx}\left( xy \right) = \frac{d}{dx}\left( c^2 \right)\]
\[ \Rightarrow x\frac{d y}{d x} + y\frac{d}{dx}\left( x \right) = 0 \left[ \text{ Using product rule } \right]\]
\[ \Rightarrow x\frac{d y}{d x} + y = 0\]
\[ \Rightarrow x\frac{d y}{d x} = - y\]
\[ \Rightarrow \frac{d y}{d x} = - \frac{y}{x}\]