Mister Exam

Lang:

The derivative of the function/ 2/x^3

Derivative of 2/x^3

The solution

You have entered [src]

2 
--
 3
x

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

d /2 \
--|--|
dx| 3|
  \x /

$$\frac{d}{d x} \frac{2}{x^{3}}$$

Transform

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: $- \frac{6}{x^{4}}$

The answer is:

$- \frac{6}{x^{4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-6 
---
  4
 x

$$- \frac{6}{x^{4}}$$

Simplify

The second derivative [src]

24
--
 5
x

$$\frac{24}{x^{5}}$$

Simplify

The third derivative [src]

-120 
-----
   6 
  x

$$- \frac{120}{x^{6}}$$

Simplify

The graph

Derivative of 2/x^3