Mister Exam

Other calculators


1/(x^2-3)

Derivative of 1/(x^2-3)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
  1   
------
 2    
x  - 3
$$\frac{1}{x^{2} - 3}$$
1/(x^2 - 3)
Detail solution
  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
   -2*x  
---------
        2
/ 2    \ 
\x  - 3/ 
$$- \frac{2 x}{\left(x^{2} - 3\right)^{2}}$$
The second derivative [src]
  /          2 \
  |       4*x  |
2*|-1 + -------|
  |           2|
  \     -3 + x /
----------------
            2   
   /      2\    
   \-3 + x /    
$$\frac{2 \left(\frac{4 x^{2}}{x^{2} - 3} - 1\right)}{\left(x^{2} - 3\right)^{2}}$$
The third derivative [src]
     /         2 \
     |      2*x  |
24*x*|1 - -------|
     |          2|
     \    -3 + x /
------------------
             3    
    /      2\     
    \-3 + x /     
$$\frac{24 x \left(- \frac{2 x^{2}}{x^{2} - 3} + 1\right)}{\left(x^{2} - 3\right)^{3}}$$
The graph
Derivative of 1/(x^2-3)