Derivative of 1/x^8

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1 
--
 8
x

$$\frac{1}{x^{8}}$$

1/(x^8)

Detail solution

Let $u = x^{8}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{8}$ :
1. Apply the power rule: $x^{8}$ goes to $8 x^{7}$
The result of the chain rule is:

$- \frac{8}{x^{9}}$

The answer is:

$- \frac{8}{x^{9}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-8  
----
   8
x*x

$$- \frac{8}{x x^{8}}$$

Simplify

The second derivative [src]

 72
---
 10
x

$$\frac{72}{x^{10}}$$

Simplify

The third derivative [src]

-720 
-----
  11 
 x

$$- \frac{720}{x^{11}}$$

Simplify

The graph