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Derivative of:
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Identical expressions
log(x^ two + three)
logarithm of (x squared plus 3)
logarithm of (x to the power of two plus three)
log(x2+3)
logx2+3
log(x²+3)
log(x to the power of 2+3)
logx^2+3
Similar expressions
log(x^2-3)

The derivative of the function/ log(x^2+3)

Derivative of log(x^2+3)

The solution

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   / 2    \
log\x  + 3/

$$\log{\left(x^{2} + 3 \right)}$$

log(x^2 + 3)

Detail solution

Let $u = x^{2} + 3$ .
The derivative of $\log{\left(u \right)}$ is $\frac{1}{u}$ .
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x^{2} + 3\right)$ :
1. Differentiate $x^{2} + 3$ term by term:
  1. Apply the power rule: $x^{2}$ goes to $2 x$
  2. The derivative of the constant $3$ is zero.
  The result is: $2 x$
The result of the chain rule is:

$\frac{2 x}{x^{2} + 3}$
Now simplify:

$\frac{2 x}{x^{2} + 3}$

The answer is:

$\frac{2 x}{x^{2} + 3}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2*x  
------
 2    
x  + 3

$$\frac{2 x}{x^{2} + 3}$$

Simplify

The second derivative [src]

  /        2 \
  |     2*x  |
2*|1 - ------|
  |         2|
  \    3 + x /
--------------
         2    
    3 + x

$$\frac{2 \left(- \frac{2 x^{2}}{x^{2} + 3} + 1\right)}{x^{2} + 3}$$

Simplify

The third derivative [src]

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

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

Simplify

The graph

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Derivative of log(x^2+3)

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The solution