Derivative of 1/x^5

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1 
--
 5
x

$$\frac{1}{x^{5}}$$

1/(x^5)

Detail solution

Let $u = x^{5}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{5}$ :
1. Apply the power rule: $x^{5}$ goes to $5 x^{4}$
The result of the chain rule is:

$- \frac{5}{x^{6}}$

The answer is:

$- \frac{5}{x^{6}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-5  
----
   5
x*x

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

Simplify

The second derivative [src]

30
--
 7
x

$$\frac{30}{x^{7}}$$

Simplify

The third derivative [src]

-210 
-----
   8 
  x

$$- \frac{210}{x^{8}}$$

Simplify

The graph