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

Derivative of log(y^2-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
   / 2    \
log\y  - 1/
log⁡(y2−1)\log{\left(y^{2} - 1 \right)} 
log(y^2 - 1)
Detail solution

  1. Let u=y2−1u = y^{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 ddy(y2−1)\frac{d}{d y} \left(y^{2} - 1\right):

    1. Differentiate y2−1y^{2} - 1 term by term:

      1. Apply the power rule: y2y^{2} goes to 2y2 y

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

      The result is: 2y2 y

    The result of the chain rule is:

    2yy2−1\frac{2 y}{y^{2} - 1}

  4. Now simplify:

    2yy2−1\frac{2 y}{y^{2} - 1}

The answer is:

2yy2−1\frac{2 y}{y^{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*y  
------
 2    
y  - 1
2yy2−1\frac{2 y}{y^{2} - 1}
Simplify
The second derivative [src] 
  /         2 \
  |      2*y  |
2*|1 - -------|
  |          2|
  \    -1 + y /
---------------
          2    
    -1 + y
2(−2y2y2−1+1)y2−1\frac{2 \left(- \frac{2 y^{2}}{y^{2} - 1} + 1\right)}{y^{2} - 1}
Simplify
The third derivative [src] 
    /          2 \
    |       4*y  |
4*y*|-3 + -------|
    |           2|
    \     -1 + y /
------------------
             2    
    /      2\     
    \-1 + y /
4y(4y2y2−1−3)(y2−1)2\frac{4 y \left(\frac{4 y^{2}}{y^{2} - 1} - 3\right)}{\left(y^{2} - 1\right)^{2}}
Simplify
The graph
Derivative of log(y^2-1)
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