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Question: Answered & Verified by Expert
If $x y=\tan ^{-1}(x y)+\cot ^{-1}(x y)$, then $\frac{d y}{d x}$ is equal
to
MathematicsDifferential EquationsMHT CETMHT CET 2009
Options:
  • A $\frac{y}{x}$
  • B $-\frac{y}{x}$
  • C $\frac{x}{y}$
  • D $-\frac{x}{y}$
Solution:
1104 Upvotes Verified Answer
The correct answer is: $-\frac{y}{x}$
$x y=\tan ^{-1}(x y)+\cot ^{-1}(x y)=\frac{\pi}{2}$
$\Rightarrow \quad x y=\frac{\pi}{2}$
$\therefore \quad x \frac{d y}{d x}+y=0$
$\Rightarrow \quad \frac{d y}{d x}=\frac{-y}{x}$

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