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log(x^2-1)

Derivative of log(x^2-1)

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

The graph:

from to

Piecewise:

The solution

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

  2. The derivative of is .

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