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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

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The solution

You have entered [src] 
log(x + 1)
log⁡(x+1)\log{\left(x + 1 \right)} 
d             
--(log(x + 1))
dx
ddxlog⁡(x+1)\frac{d}{d x} \log{\left(x + 1 \right)}
Transform
Detail solution

  1. Let u=x+1u = x + 1.

  2. The derivative of log⁡(u)\log{\left(u \right)} is 1u\frac{1}{u}.

  3. Then, apply the chain rule. Multiply by ddx(x+1)\frac{d}{d x} \left(x + 1\right):

    1. Differentiate x+1x + 1 term by term:

      1. Apply the power rule: xx goes to 11

      2. The derivative of the constant 11 is zero.

      The result is: 11

    The result of the chain rule is:

    1x+1\frac{1}{x + 1}

  4. Now simplify:

    1x+1\frac{1}{x + 1}

The answer is:

1x+1\frac{1}{x + 1}

The graph
02468-8-6-4-2-1010-2020
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1  
-----
x + 1
1x+1\frac{1}{x + 1}
Simplify
The second derivative [src] 
  -1    
--------
       2
(1 + x)
−1(x+1)2- \frac{1}{\left(x + 1\right)^{2}}
Simplify
The third derivative [src] 
   2    
--------
       3
(1 + x)
2(x+1)3\frac{2}{\left(x + 1\right)^{3}}
Simplify
The graph
Derivative of ln(x+1)
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