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The derivative of the function/ ln(2x^(2)-5)

Derivative of ln(2x^(2)-5)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
   /   2    \
log\2*x  - 5/
log⁡(2x2−5)\log{\left(2 x^{2} - 5 \right)} 
log(2*x^2 - 5)
Detail solution

  1. Let u=2x2−5u = 2 x^{2} - 5.

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

  3. Then, apply the chain rule. Multiply by ddx(2x2−5)\frac{d}{d x} \left(2 x^{2} - 5\right):

    1. Differentiate 2x2−52 x^{2} - 5 term by term:

      1. 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: 4x4 x

      2. The derivative of the constant −5-5 is zero.

      The result is: 4x4 x

    The result of the chain rule is:

    4x2x2−5\frac{4 x}{2 x^{2} - 5}

  4. Now simplify:

    4x2x2−5\frac{4 x}{2 x^{2} - 5}

The answer is:

4x2x2−5\frac{4 x}{2 x^{2} - 5}

The graph
02468-8-6-4-2-1010-5050
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  4*x   
--------
   2    
2*x  - 5
4x2x2−5\frac{4 x}{2 x^{2} - 5}
Simplify
The second derivative [src] 
  /          2  \
  |       4*x   |
4*|1 - ---------|
  |            2|
  \    -5 + 2*x /
-----------------
            2    
    -5 + 2*x
4(−4x22x2−5+1)2x2−5\frac{4 \left(- \frac{4 x^{2}}{2 x^{2} - 5} + 1\right)}{2 x^{2} - 5}
Simplify
The third derivative [src] 
     /           2  \
     |        8*x   |
16*x*|-3 + ---------|
     |             2|
     \     -5 + 2*x /
---------------------
                2    
     /        2\     
     \-5 + 2*x /
16x(8x22x2−5−3)(2x2−5)2\frac{16 x \left(\frac{8 x^{2}}{2 x^{2} - 5} - 3\right)}{\left(2 x^{2} - 5\right)^{2}}
Simplify
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