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  4. Find the derivative of √2x+2√x-(1/x) ?

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Q. Find the derivative of $ \sqrt{2}x+2\sqrt{x}-\frac{1}{x} $ ?

J & K CETJ & K CET 2014Limits and Derivatives

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) $