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Mathematics · 2023 · 2 marks
CBSE 2023 · Region 4 · Set 3 · Q21
If xy = e^x - y, then show that dy/dx=(y ( x -1))/(x ( y +1)).
If $\displaystyle \mathrm{xy}=\mathrm{e}^{\mathrm{x}-\mathrm{y}}$, then show that $\displaystyle \frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}(\mathrm{x}-1)}{\mathrm{x}(\mathrm{y}+1)}$.
Marking-scheme solution
Given $\displaystyle \mathrm{xy}=\mathrm{e}^{\mathrm{x}-\mathrm{y}}$, gives $\displaystyle \mathrm{x}-\mathrm{y}=\log \mathrm{x}+\log \mathrm{y}$
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CBSE Class 12 Mathematics past-paper question from the 2023 board exam, with the answer as CBSE’s own marking scheme gives it. Where our answers come from.