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ln(x^2+5)

Derivative of ln(x^2+5)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
   / 2    \
log\x  + 5/
$$\log{\left(x^{2} + 5 \right)}$$
d /   / 2    \\
--\log\x  + 5//
dx             
$$\frac{d}{d x} \log{\left(x^{2} + 5 \right)}$$
Detail solution
  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:


The answer is:

The graph
The first derivative [src]
 2*x  
------
 2    
x  + 5
$$\frac{2 x}{x^{2} + 5}$$
The second derivative [src]
  /        2 \
  |     2*x  |
2*|1 - ------|
  |         2|
  \    5 + x /
--------------
         2    
    5 + x     
$$\frac{2 \left(- \frac{2 x^{2}}{x^{2} + 5} + 1\right)}{x^{2} + 5}$$
The third derivative [src]
    /         2 \
    |      4*x  |
4*x*|-3 + ------|
    |          2|
    \     5 + x /
-----------------
            2    
    /     2\     
    \5 + x /     
$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} + 5} - 3\right)}{\left(x^{2} + 5\right)^{2}}$$
The graph
Derivative of ln(x^2+5)