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Derivative of:
Derivative of (x^2-2*x)/(3+x^2)
Derivative of (sin(2*x))'
Derivative of sin(4*x-1)^(3)
Derivative of log(9*x)
Identical expressions
ln(one /(x^ three))
ln(1 divide by (x cubed ))
ln(one divide by (x to the power of three))
ln(1/(x3))
ln1/x3
ln(1/(x³))
ln(1/(x to the power of 3))
ln1/x^3
ln(1 divide by (x^3))

The derivative of the function/ ln(1/(x^3))

Derivative of ln(1/(x^3))

The solution

You have entered [src]

   /1 \
log|--|
   | 3|
   \x /

\log{\left(\frac{1}{x^{3}} \right)}

log(1/(x^3))

Detail solution

Let $u = \frac{1}{x^{3}}$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \frac{1}{x^{3}}$ :
1. Let $u = x^{3}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. 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:
  
  $- \frac{3}{x^{4}}$
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