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ln(x+1)
The derivative of the function/ ln(x+1)

Derivative of ln(x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
log(x + 1)
$$\log{\left(x + 1 \right)}$$ 
d             
--(log(x + 1))
dx
$$\frac{d}{d x} \log{\left(x + 1 \right)}$$
Transform
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
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1  
-----
x + 1
$$\frac{1}{x + 1}$$
Simplify
The second derivative [src] 
  -1    
--------
       2
(1 + x)
$$- \frac{1}{\left(x + 1\right)^{2}}$$
Simplify
The third derivative [src] 
   2    
--------
       3
(1 + x)
$$\frac{2}{\left(x + 1\right)^{3}}$$
Simplify
The graph
Derivative of ln(x+1)
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