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

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

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

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The solution

You have entered [src] 
       / 2    \
x + log\x  - 4/
x+log⁡(x2−4)x + \log{\left(x^{2} - 4 \right)} 
x + log(x^2 - 4)
Detail solution

  1. Differentiate x+log⁡(x2−4)x + \log{\left(x^{2} - 4 \right)} term by term:

    1. Apply the power rule: xx goes to 11

    2. Let u=x2−4u = x^{2} - 4.

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

    4. Then, apply the chain rule. Multiply by ddx(x2−4)\frac{d}{d x} \left(x^{2} - 4\right):

      1. Differentiate x2−4x^{2} - 4 term by term:

        1. Apply the power rule: x2x^{2} goes to 2x2 x

        2. The derivative of the constant −4-4 is zero.

        The result is: 2x2 x

      The result of the chain rule is:

      2xx2−4\frac{2 x}{x^{2} - 4}

    The result is: 2xx2−4+1\frac{2 x}{x^{2} - 4} + 1

  2. Now simplify:

    x2+2x−4x2−4\frac{x^{2} + 2 x - 4}{x^{2} - 4}

The answer is:

x2+2x−4x2−4\frac{x^{2} + 2 x - 4}{x^{2} - 4}

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  
1 + ------
     2    
    x  - 4
2xx2−4+1\frac{2 x}{x^{2} - 4} + 1
Simplify
The second derivative [src] 
  /         2 \
  |      2*x  |
2*|1 - -------|
  |          2|
  \    -4 + x /
---------------
          2    
    -4 + x
2(−2x2x2−4+1)x2−4\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 /
4x(4x2x2−4−3)(x2−4)2\frac{4 x \left(\frac{4 x^{2}}{x^{2} - 4} - 3\right)}{\left(x^{2} - 4\right)^{2}}
Simplify
The graph
Derivative of x+ln(x^2-4)
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