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Graphing y =:
log(x^2-1)
Identical expressions
log(x^ two - one)
logarithm of (x squared minus 1)
logarithm of (x to the power of two minus one)
log(x2-1)
logx2-1
log(x²-1)
log(x to the power of 2-1)
logx^2-1
Similar expressions
log(x^2+1)

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

Derivative of log(x^2-1)

The solution

You have entered [src]

   / 2    \
log\x  - 1/

$$\log{\left(x^{2} - 1 \right)}$$

log(x^2 - 1)

Detail solution

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

$\frac{2 x}{x^{2} - 1}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2*x  
------
 2    
x  - 1

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

Simplify

The second derivative [src]

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

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

Simplify

The third derivative [src]

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

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

Simplify

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Derivative of log(x^2-1)

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The solution