A) \[\frac{1}{2[\sqrt{(x-a)}+\sqrt{(x-b)}]}\]
B) \[\frac{1}{2\sqrt{(x-a)(x-b)}}\]
C) \[\frac{1}{\sqrt{(x-a)(x-b)}}\]
D) None of these
Correct Answer: B
Solution :
\[\frac{d}{dx}\log (\sqrt{x-a}+\sqrt{x-b})\] \[=\left( \frac{1}{\sqrt{x-a}+\sqrt{x-b}} \right)\frac{1}{2}\left[ \frac{1}{\sqrt{x-a}}+\frac{1}{\sqrt{x-b}} \right]\] \[=\left[ \frac{\sqrt{x-a}+\sqrt{x-b}}{\sqrt{x-a}+\sqrt{x-b}} \right]\frac{1}{2\sqrt{(x-a)(x-b)}}\]\[=\frac{1}{2\sqrt{(x-a)(x-b)}}\].
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