A) \[\sqrt{2}+1/\sqrt{x}(1-1/2x)\]
B) \[\sqrt{2}-1/\sqrt{x}(1+1/2x)\]
C) \[\sqrt{2}-1/\sqrt{x}(1-1/2x)\]
D) \[\sqrt{2}+1/\sqrt{x}(1+1/2x)\]
Correct Answer: D
Solution :
The derivative of \[\sqrt{2}x+2\sqrt{x}-\frac{1}{\sqrt{x}}\] \[=\sqrt{2}+2\cdot \frac{1}{2}{{x}^{\frac{1}{2}-1}}+\frac{1}{2}{{x}^{-\frac{1}{2}-1}}\] \[=\sqrt{2}+{{x}^{\frac{-1}{2}}}+\frac{1}{2}{{x}^{\frac{-3}{2}}}\] \[=\sqrt{2}+\frac{1}{\sqrt{x}}+\frac{1}{2x\sqrt{x}}\] \[=\sqrt{2}+\frac{1}{\sqrt{x}}\left( 1+\frac{1}{2x} \right)\]
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