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Integral of d{x}:
1/(x^2-3)
Identical expressions
one /(x^ two - three)
1 divide by (x squared minus 3)
one divide by (x to the power of two minus three)
1/(x2-3)
1/x2-3
1/(x²-3)
1/(x to the power of 2-3)
1/x^2-3
1 divide by (x^2-3)
Similar expressions
1/(x^2+3)

The derivative of the function/ 1/(x^2-3)

Derivative of 1/(x^2-3)

The solution

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  1   
------
 2    
x  - 3

$$\frac{1}{x^{2} - 3}$$

1/(x^2 - 3)

Detail solution

Let $u = x^{2} - 3$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 3\right)$ :
1. Differentiate $x^{2} - 3$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $-3$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$- \frac{2 x}{\left(x^{2} - 3\right)^{2}}$
Now simplify:

$- \frac{2 x}{\left(x^{2} - 3\right)^{2}}$

The answer is:

$- \frac{2 x}{\left(x^{2} - 3\right)^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

   -2*x  
---------
        2
/ 2    \ 
\x  - 3/

$$- \frac{2 x}{\left(x^{2} - 3\right)^{2}}$$

Simplify

The second derivative [src]

  /          2 \
  |       4*x  |
2*|-1 + -------|
  |           2|
  \     -3 + x /
----------------
            2   
   /      2\    
   \-3 + x /

$$\frac{2 \left(\frac{4 x^{2}}{x^{2} - 3} - 1\right)}{\left(x^{2} - 3\right)^{2}}$$

Simplify

The third derivative [src]

     /         2 \
     |      2*x  |
24*x*|1 - -------|
     |          2|
     \    -3 + x /
------------------
             3    
    /      2\     
    \-3 + x /

$$\frac{24 x \left(- \frac{2 x^{2}}{x^{2} - 3} + 1\right)}{\left(x^{2} - 3\right)^{3}}$$

Simplify

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Derivative of 1/(x^2-3)

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The solution