Derivative of log(x^-1)

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$$\log{\left(\frac{1}{x} \right)}$$

log(1/x)

Detail solution

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

$- \frac{1}{x}$

The answer is:

$- \frac{1}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-1 
---
 x

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

Simplify

The second derivative [src]

1 
--
 2
x

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

Simplify

The third derivative [src]

-2 
---
  3
 x

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

Simplify

The graph