What is the derivative of 1+1/(sqrt(x)) ?

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

What is the first derivative of 1+1/(sqrt(x)) ?

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

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

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

Solution steps

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

Apply the Sum/Difference Rule:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - \frac{1}{2 x ^{\frac{3}{2}}}

Simplify

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

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