Derivative of ln(x^3)

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   / 3\
log\x /

\log{\left(x^{3} \right)}

log(x^3)

Detail solution

Let $u = x^{3}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{3}$ :
1. Apply the power rule: $x^{3}$ goes to $3 x^{2}$
The result of the chain rule is:

$\frac{3}{x}$

The answer is:

\frac{3}{x}

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

3
-
x

\frac{3}{x}

Simplify

The second derivative [src]

-3 
---
  2
 x

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

Simplify

The third derivative [src]

6 
--
 3
x

\frac{6}{x^{3}}

Simplify

The graph