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derivative of sqrt(2x)+1/(sqrt(2x))

Solution

\frac{d}{d x} (2 x + \frac{1}{2 x})

Solution

\frac{1}{2 x} - \frac{1}{2 2 x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (2 x + \frac{1}{2 x})

Apply the Sum/Difference Rule:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{d}{d x} (2 x) + \frac{d}{d x} (\frac{1}{2 x})

\frac{d}{d x} (2 x) = \frac{1}{2 x}

\frac{d}{d x} (\frac{1}{2 x}) = - \frac{1}{2 2 x ^{\frac{3}{2}}}

= \frac{1}{2 x} - \frac{1}{2 2 x ^{\frac{3}{2}}}

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Frequently Asked Questions (FAQ)

What is the derivative of sqrt(2x)+1/(sqrt(2x)) ?
The derivative of sqrt(2x)+1/(sqrt(2x)) is 1/(sqrt(2)\sqrt{x)}-1/(2sqrt(2)x^{3/2)}
What is the first derivative of sqrt(2x)+1/(sqrt(2x)) ?
The first derivative of sqrt(2x)+1/(sqrt(2x)) is 1/(sqrt(2)\sqrt{x)}-1/(2sqrt(2)x^{3/2)}