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

Derivative of log(x+2)

The solution

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log(x + 2)

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

log(x + 2)

Detail solution

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

$\frac{1}{x + 2}$
Now simplify:

$\frac{1}{x + 2}$

The answer is:

$\frac{1}{x + 2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  1  
-----
x + 2

$$\frac{1}{x + 2}$$

Simplify

The second derivative [src]

  -1    
--------
       2
(2 + x)

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

Simplify

The third derivative [src]

   2    
--------
       3
(2 + x)

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

Simplify

The graph

Derivative of log(x+2)