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

Derivative of ln(1-x^2)

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

The graph:

from to

Piecewise:

The solution

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

  1. Let .

  2. The derivative of is .

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

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 -2*x 
------
     2
1 - x
$$- \frac{2 x}{1 - x^{2}}$$
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
The graph
Derivative of ln(1-x^2)
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