MHT CET · Maths · Differentiation
If \(\mathrm{u}=\log (\sqrt{x-1}-\sqrt{x+1})\) and \(\mathrm{v}=\sqrt{x+1}+\sqrt{x-1}\) then \(\frac{\mathrm{du}}{\mathrm{dv}}=\ldots\).
- A u
- B v
- C \(\frac{-1}{\mathrm{u}}\)
- D \(\frac{-1}{\mathrm{v}}\)
Answer & Solution
Correct Answer
(D) \(\frac{-1}{\mathrm{v}}\)
Step-by-step Solution
Detailed explanation
\((\sqrt{x-1}-\sqrt{x+1})(\sqrt{x+1}+\sqrt{x-1}) = (x-1)-(x+1) = -2\) \(\implies (\sqrt{x-1}-\sqrt{x+1})\mathrm{v} = -2 \implies \sqrt{x-1}-\sqrt{x+1} = \frac{-2}{\mathrm{v}}\)
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