Derivative of -1/x

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-1 
---
 x

$$- \frac{1}{x}$$

d /-1 \
--|---|
dx\ x /

$$\frac{d}{d x} \left(- \frac{1}{x}\right)$$

Transform

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
So, the result is: $\frac{1}{x^{2}}$

The answer is:

$\frac{1}{x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

1 
--
 2
x

$$\frac{1}{x^{2}}$$

Simplify

The second derivative [src]

-2 
---
  3
 x

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

Simplify

The third derivative [src]

6 
--
 4
x

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

Simplify

The graph