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

Derivative of ln(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⁡(x2−1)\log{\left(x^{2} - 1 \right)} 
log(x^2 - 1)
Detail solution

  1. Let u=x2−1u = x^{2} - 1.

  2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddx(x2−1)\frac{d}{d x} \left(x^{2} - 1\right):

    1. Differentiate x2−1x^{2} - 1 term by term:

      1. Apply the power rule: x2x^{2} goes to 2x2 x

      2. The derivative of the constant −1-1 is zero.

      The result is: 2x2 x

    The result of the chain rule is:

    2xx2−1\frac{2 x}{x^{2} - 1}

  4. Now simplify:

    2xx2−1\frac{2 x}{x^{2} - 1}

The answer is:

2xx2−1\frac{2 x}{x^{2} - 1}

The graph
02468-8-6-4-2-1010-2525
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 2*x  
------
 2    
x  - 1
2xx2−1\frac{2 x}{x^{2} - 1}
Simplify
The second derivative [src] 
  /         2 \
  |      2*x  |
2*|1 - -------|
  |          2|
  \    -1 + x /
---------------
          2    
    -1 + x
2(−2x2x2−1+1)x2−1\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 /
4x(4x2x2−1−3)(x2−1)2\frac{4 x \left(\frac{4 x^{2}}{x^{2} - 1} - 3\right)}{\left(x^{2} - 1\right)^{2}}
Simplify
The graph
Derivative of ln(x^2-1)
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