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

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   /   2    \
log\2*x  - 5/

$$\log{\left(2 x^{2} - 5 \right)}$$

log(2*x^2 - 5)

Detail solution

Let $u = 2 x^{2} - 5$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(2 x^{2} - 5\right)$ :
1. Differentiate $2 x^{2} - 5$ 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: $x^{2}$ goes to $2 x$
    So, the result is: $4 x$
  2. The derivative of the constant $-5$ is zero.
  The result is: $4 x$
The result of the chain rule is:

$\frac{4 x}{2 x^{2} - 5}$
Now simplify:

$\frac{4 x}{2 x^{2} - 5}$

The answer is:

$\frac{4 x}{2 x^{2} - 5}$

The graph

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The first derivative [src]

  4*x   
--------
   2    
2*x  - 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

$$\frac{4 \left(- \frac{4 x^{2}}{2 x^{2} - 5} + 1\right)}{2 x^{2} - 5}$$

Simplify

The third derivative [src]

     /           2  \
     |        8*x   |
16*x*|-3 + ---------|
     |             2|
     \     -5 + 2*x /
---------------------
                2    
     /        2\     
     \-5 + 2*x /

$$\frac{16 x \left(\frac{8 x^{2}}{2 x^{2} - 5} - 3\right)}{\left(2 x^{2} - 5\right)^{2}}$$

Simplify

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

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The solution