Derivative of 1/sqrt(x)

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  1  
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  ___
\/ x

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

1/(sqrt(x))

Detail solution

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

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   -1    
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      ___
2*x*\/ x

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

Simplify

The second derivative [src]

  3   
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   5/2
4*x

$$\frac{3}{4 x^{\frac{5}{2}}}$$

Simplify

The third derivative [src]

 -15  
------
   7/2
8*x

$$- \frac{15}{8 x^{\frac{7}{2}}}$$

Simplify

The graph