Derivative of sqrt(1/x)

You have entered [src]

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   / 1 
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\/   x

\sqrt{\frac{1}{x}}

sqrt(1/x)

Detail solution

Let $u = \frac{1}{x}$ .
Apply the power rule: $\sqrt{u}$ goes to $\frac{1}{2 \sqrt{u}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{1}{x}$ :
1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
The result of the chain rule is:

$- \frac{1}{2 x^{2} \sqrt{\frac{1}{x}}}$

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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   2*x

- \frac{\sqrt{\frac{1}{x}}}{2 x}

Simplify

The second derivative [src]

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      2  
   4*x

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

Simplify

The third derivative [src]

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-15*  /  - 
    \/   x 
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       3   
    8*x

- \frac{15 \sqrt{\frac{1}{x}}}{8 x^{3}}

Simplify

The graph