What is the derivative of (sqrt(x)/2-2/(sqrt(x))) ?

The derivative of (sqrt(x)/2-2/(sqrt(x))) is 1/(4sqrt(x))+1/(x^{3/2)}

What is the first derivative of (sqrt(x)/2-2/(sqrt(x))) ?

The first derivative of (sqrt(x)/2-2/(sqrt(x))) is 1/(4sqrt(x))+1/(x^{3/2)}

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\frac{d}{d x} (\frac{x}{2} - \frac{2}{x})

\frac{1}{4 x} + \frac{1}{x ^{\frac{3}{2}}}

Solution steps

\frac{d}{d x} (\frac{x}{2} - \frac{2}{x})

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (\frac{x}{2}) = \frac{1}{4 x}

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

= \frac{1}{4 x} - (- \frac{1}{x ^{\frac{3}{2}}})

Simplify

= \frac{1}{4 x} + \frac{1}{x ^{\frac{3}{2}}}

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What is the derivative of (sqrt(x)/2-2/(sqrt(x))) ?
The derivative of (sqrt(x)/2-2/(sqrt(x))) is 1/(4sqrt(x))+1/(x^{3/2)}
What is the first derivative of (sqrt(x)/2-2/(sqrt(x))) ?
The first derivative of (sqrt(x)/2-2/(sqrt(x))) is 1/(4sqrt(x))+1/(x^{3/2)}