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Derivative of:
Derivative of (sin(x))^2
Derivative of e^(-x)
Derivative of sin(x)/cos(x)
Derivative of (x^2+1)^3
Limit of the function:
-1/x^3
Identical expressions
- one /x^ three
minus 1 divide by x cubed
minus one divide by x to the power of three
-1/x3
-1/x³
-1/x to the power of 3
-1 divide by x^3
Similar expressions
1/x^3

The derivative of the function/ -1/x^3

Derivative of -1/x^3

The solution

You have entered [src]

-1 
---
  3
 x

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

-1/x^3

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
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:
  
  $- \frac{3}{x^{4}}$
So, the result 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 
--
 4
x

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

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