Question

Find $\frac{dy}{dx}$ in each of the following cases:

$xy=c^2$

Answer 1

$\mathrm{We}\mathrm{have},xy=c^2$
Differentiating with respect to x, we get,
$$\begin{gathered} \frac{d}{dx}\left(xy\right)=\frac{d}{dx}\left(c^2\right) \\ \Rightarrow x\frac{\mathit{d}y}{\mathit{d}x}+y\frac{d}{dx}\left(x\right)=0\left[\mathrm{Using}\mathrm{product}\mathrm{rule}\right] \\ \Rightarrow x\frac{\mathit{d}y}{\mathit{d}x}+y=0 \\ \Rightarrow x\frac{\mathit{d}y}{\mathit{d}x}=-y \\ \Rightarrow \frac{\mathit{d}y}{\mathit{d}x}=-\frac{y}{x} \end{gathered}$$