Mister Exam

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Derivative of 1/x^6

You have entered [src]

1 
--
 6
x

$$\frac{1}{x^{6}}$$

1/(x^6)

Detail solution

Let $u = x^{6}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} x^{6}$ :
1. Apply the power rule: $x^{6}$ goes to $6 x^{5}$
The result of the chain rule is:

$- \frac{6}{x^{7}}$

The answer is:

$- \frac{6}{x^{7}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-6  
----
   6
x*x

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

Simplify

The second derivative [src]

42
--
 8
x

$$\frac{42}{x^{8}}$$

Simplify

The third derivative [src]

-336 
-----
   9 
  x

$$- \frac{336}{x^{9}}$$

Simplify

The graph