Derivative of 1/x³

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1 
--
 3
x

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

1/(x^3)

Detail solution

Let $u = x^{3}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
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 answer is:

$- \frac{3}{x^{4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-3  
----
   3
x*x

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

Simplify

The second derivative [src]

12
--
 5
x

$$\frac{12}{x^{5}}$$

Simplify

The third derivative [src]

-60 
----
  6 
 x

$$- \frac{60}{x^{6}}$$

Simplify

The graph