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The derivative of the function/ y=x/x²-1

Derivative of y=x/x²-1

The solution

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x     
-- - 1
 2    
x

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

x/x^2 - 1

Detail solution

Differentiate $\frac{x}{x^{2}} - 1$ term by term:
1. Apply the quotient rule, which is:
  
  $\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$
  
  $f{\left(x \right)} = x$ and $g{\left(x \right)} = x^{2}$ .
  
  To find $\frac{d}{d x} f{\left(x \right)}$ :
  1. Apply the power rule: $x$ goes to $1$
  To find $\frac{d}{d x} g{\left(x \right)}$ :
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  Now plug in to the quotient rule:
  
  $- \frac{1}{x^{2}}$
2. The derivative of the constant $-1$ is zero.
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 
-- - --
 2    2
x    x

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

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

Derivative of y=x/x²-1