What is the derivative of f(x)=sqrt(x)-1/(sqrt(x)) ?

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

What is the first derivative of f(x)=sqrt(x)-1/(sqrt(x)) ?

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

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derivative of

f (x) = x - \frac{1}{x}

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

Solution steps

\frac{d}{d x} (x - \frac{1}{x})

Apply the Sum/Difference Rule:

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

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

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

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

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

Simplify

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

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