Derivative of log(sqrt(x))

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log\\/ x /

$$\log{\left(\sqrt{x} \right)}$$

log(sqrt(x))

Detail solution

Let $u = \sqrt{x}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
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:

$\frac{1}{2 x}$

The answer is:

$\frac{1}{2 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 1 
---
2*x

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

Simplify

The second derivative [src]

-1  
----
   2
2*x

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

Simplify

The third derivative [src]

1 
--
 3
x

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

Simplify

The graph