Mister Exam

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Derivative of 1/x^4

You have entered [src]

1 
--
 4
x

$$\frac{1}{x^{4}}$$

1/(x^4)

Detail solution

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

$- \frac{4}{x^{5}}$

The answer is:

$- \frac{4}{x^{5}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-4  
----
   4
x*x

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

Simplify

The second derivative [src]

20
--
 6
x

$$\frac{20}{x^{6}}$$

Simplify

The third derivative [src]

-120 
-----
   7 
  x

$$- \frac{120}{x^{7}}$$

Simplify

The graph