MCQ
${d \over {dx}}\log (\sqrt {x - a} + \sqrt {x - b} ) = $
- A${1 \over {2[\sqrt {(x - a)} + \sqrt {(x - b)} ]}}$
- ✓${1 \over {2\sqrt {(x - a)(x - b)} }}$
- C${1 \over {\sqrt {(x - a)(x - b)} }}$
- DNone of these
$ = \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)} }}$.
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$f(x)=\left|\begin{array}{ccc} \sin ^{2} x & 1+\cos ^{2} x & \cos 2 x \\ 1+\sin ^{2} x & \cos ^{2} x & \cos 2 x \\ \sin ^{2} x & \cos ^{2} x & \sin 2 x \end{array}\right|, x \in R \text { is }$