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Derivative of:
Derivative of log(2)
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Derivative of cos(1/x)
Integral of d{x}:
log(1-x^2)
Limit of the function:
log(1-x^2)
Identical expressions
log(one -x^ two)
logarithm of (1 minus x squared )
logarithm of (one minus x to the power of two)
log(1-x2)
log1-x2
log(1-x²)
log(1-x to the power of 2)
log1-x^2
Similar expressions
log(1+x^2)

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

Derivative of log(1-x^2)

The solution

You have entered [src]

   /     2\
log\1 - x /

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

d /   /     2\\
--\log\1 - x //
dx

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

Transform

Detail solution

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

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

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Derivative of log(1-x^2)

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The solution