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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

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The solution

You have entered [src] 
   /     2\
log\1 - x /
log⁡(1−x2)\log{\left(1 - x^{2} \right)} 
log(1 - x^2)
Detail solution

  1. Let u=1−x2u = 1 - x^{2}.

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

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

    1. Differentiate 1−x21 - x^{2} term by term:

      1. The derivative of the constant 11 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: x2x^{2} goes to 2x2 x

        So, the result is: −2x- 2 x

      The result is: −2x- 2 x

    The result of the chain rule is:

    −2x1−x2- \frac{2 x}{1 - x^{2}}

  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
1 - x
−2x1−x2- \frac{2 x}{1 - x^{2}}
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(1-x^2)
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