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Graphing y =:
ln(x^2+5)
Identical expressions
ln(x^ two + five)
ln(x squared plus 5)
ln(x to the power of two plus five)
ln(x2+5)
lnx2+5
ln(x²+5)
ln(x to the power of 2+5)
lnx^2+5
Similar expressions
ln(x^2-5)

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

Derivative of ln(x^2+5)

The solution

You have entered [src]

   / 2    \
log\x  + 5/

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

d /   / 2    \\
--\log\x  + 5//
dx

$$\frac{d}{d x} \log{\left(x^{2} + 5 \right)}$$

Transform

Detail solution

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

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

$\frac{2 x}{x^{2} + 5}$

The answer is:

$\frac{2 x}{x^{2} + 5}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2*x  
------
 2    
x  + 5

$$\frac{2 x}{x^{2} + 5}$$

Simplify

The second derivative [src]

  /        2 \
  |     2*x  |
2*|1 - ------|
  |         2|
  \    5 + x /
--------------
         2    
    5 + x

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

Simplify

The third derivative [src]

    /         2 \
    |      4*x  |
4*x*|-3 + ------|
    |          2|
    \     5 + x /
-----------------
            2    
    /     2\     
    \5 + x /

$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} + 5} - 3\right)}{\left(x^{2} + 5\right)^{2}}$$

Simplify

The graph

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Derivative of ln(x^2+5)

The graph:

Piecewise:

The solution