Mister Exam

Derivative of log(x+1)/(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)
----------
  x + 1   
$$\frac{\log{\left(x + 1 \right)}}{x + 1}$$
log(x + 1)/(x + 1)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    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:

    To find :

    1. Differentiate term by term:

      1. The derivative of the constant is zero.

      2. Apply the power rule: goes to

      The result is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
   1       log(x + 1)
-------- - ----------
       2           2 
(x + 1)     (x + 1)  
$$- \frac{\log{\left(x + 1 \right)}}{\left(x + 1\right)^{2}} + \frac{1}{\left(x + 1\right)^{2}}$$
The second derivative [src]
-3 + 2*log(1 + x)
-----------------
            3    
     (1 + x)     
$$\frac{2 \log{\left(x + 1 \right)} - 3}{\left(x + 1\right)^{3}}$$
The third derivative [src]
11 - 6*log(1 + x)
-----------------
            4    
     (1 + x)     
$$\frac{11 - 6 \log{\left(x + 1 \right)}}{\left(x + 1\right)^{4}}$$
The graph
Derivative of log(x+1)/(x+1)