Question

If $xy={\tan }^{-1}\left(xy\right)+{\cot }^{-1}\left(xy\right)$, then $\frac{dy}{dx}$ is equal to

• A. $\frac{y}{x}$
• B. $-\frac{y}{x}$
• C. $\frac{x}{y}$
• D. $-\frac{x}{y}$

Answer 1

The correct option is B $-\frac{y}{x}$

$xy={\tan }^{-1}\left(xy\right)+{\cot }^{-1}\left(xy\right)=\frac{\pi }{2}$
$\Rightarrow xy=\frac{\pi }{2}$
$\therefore x\frac{dy}{dx}+y=0$
$\Rightarrow \frac{dy}{dx}=\frac{-y}{x}$