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Derivative of x+ln(x^2-4)
Graphing y =:
x+ln(x^2-4)
Identical expressions
x+ln(x^ two - four)
x plus ln(x squared minus 4)
x plus ln(x to the power of two minus four)
x+ln(x2-4)
x+lnx2-4
x+ln(x²-4)
x+ln(x to the power of 2-4)
x+lnx^2-4
Similar expressions
x-ln(x^2-4)
x+ln(x^2+4)

The derivative of the function/ x+ln(x^2-4)

Derivative of x+ln(x^2-4)

The solution

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       / 2    \
x + log\x  - 4/

$$x + \log{\left(x^{2} - 4 \right)}$$

x + log(x^2 - 4)

Detail solution

Differentiate $x + \log{\left(x^{2} - 4 \right)}$ term by term:
1. Apply the power rule: $x$ goes to $1$
2. Let $u = x^{2} - 4$ .
3. The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
4. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} - 4\right)$ :
  1. Differentiate $x^{2} - 4$ term by term:
    1. Apply the power rule: $x^{2}$ goes to $2 x$
    2. The derivative of the constant $-4$ is zero.
    The result is: $2 x$
  The result of the chain rule is:
  
  $\frac{2 x}{x^{2} - 4}$
The result is: $\frac{2 x}{x^{2} - 4} + 1$
Now simplify:

$\frac{x^{2} + 2 x - 4}{x^{2} - 4}$

The answer is:

$\frac{x^{2} + 2 x - 4}{x^{2} - 4}$

The graph

Plot the graph f(x)

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The first derivative [src]

     2*x  
1 + ------
     2    
    x  - 4

$$\frac{2 x}{x^{2} - 4} + 1$$

Simplify

The second derivative [src]

  /         2 \
  |      2*x  |
2*|1 - -------|
  |          2|
  \    -4 + x /
---------------
          2    
    -4 + x

$$\frac{2 \left(- \frac{2 x^{2}}{x^{2} - 4} + 1\right)}{x^{2} - 4}$$

Simplify

The third derivative [src]

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

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

Simplify

The graph

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Derivative of x+ln(x^2-4)

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The solution