Mister Exam

Derivative of log(1+x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
log(1 + x)
$$\log{\left(x + 1 \right)}$$
log(1 + x)
Detail solution
  1. Let .

  2. The derivative of is .

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    The result of the chain rule is:


The answer is:

The graph
The first derivative [src]
  1  
-----
1 + x
$$\frac{1}{x + 1}$$
The second derivative [src]
  -1    
--------
       2
(1 + x) 
$$- \frac{1}{\left(x + 1\right)^{2}}$$
The third derivative [src]
   2    
--------
       3
(1 + x) 
$$\frac{2}{\left(x + 1\right)^{3}}$$
The graph
Derivative of log(1+x)