Derivative of ln(x^7)

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   / 7\
log\x /

$$\log{\left(x^{7} \right)}$$

log(x^7)

Detail solution

Let $u = x^{7}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{7}$ :
1. Apply the power rule: $x^{7}$ goes to $7 x^{6}$
The result of the chain rule is:

$\frac{7}{x}$

The answer is:

$\frac{7}{x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

7
-
x

$$\frac{7}{x}$$

Simplify

The second derivative [src]

-7 
---
  2
 x

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

Simplify

The third derivative [src]

14
--
 3
x

$$\frac{14}{x^{3}}$$

Simplify