Derivative of ln(x^2-9)

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   / 2    \
log\x  - 9/

$$\log{\left(x^{2} - 9 \right)}$$

d /   / 2    \\
--\log\x  - 9//
dx

$$\frac{d}{d x} \log{\left(x^{2} - 9 \right)}$$

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Detail solution

Let $u = x^{2} - 9$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 9\right)$ :
1. Differentiate $x^{2} - 9$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $\left(-1\right) 9$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$\frac{2 x}{x^{2} - 9}$
Now simplify:

$\frac{2 x}{x^{2} - 9}$

The answer is:

$\frac{2 x}{x^{2} - 9}$

The graph

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The first derivative [src]

 2*x  
------
 2    
x  - 9

$$\frac{2 x}{x^{2} - 9}$$

Simplify

The second derivative [src]

  /         2 \
  |      2*x  |
2*|1 - -------|
  |          2|
  \    -9 + x /
---------------
          2    
    -9 + x

$$\frac{2 \left(- \frac{2 x^{2}}{x^{2} - 9} + 1\right)}{x^{2} - 9}$$

Simplify

The third derivative [src]

    /          2 \
    |       4*x  |
4*x*|-3 + -------|
    |           2|
    \     -9 + x /
------------------
             2    
    /      2\     
    \-9 + x /

$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} - 9} - 3\right)}{\left(x^{2} - 9\right)^{2}}$$

Simplify

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Derivative of ln(x^2-9)

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