Mister Exam

Derivative of (x+5)/(x+1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
x + 5
-----
x + 1
$$\frac{x + 5}{x + 1}$$
(x + 5)/(x + 1)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    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:

    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:


The answer is:

The graph
The first derivative [src]
  1      x + 5  
----- - --------
x + 1          2
        (x + 1) 
$$\frac{1}{x + 1} - \frac{x + 5}{\left(x + 1\right)^{2}}$$
The second derivative [src]
  /     5 + x\
2*|-1 + -----|
  \     1 + x/
--------------
          2   
   (1 + x)    
$$\frac{2 \left(-1 + \frac{x + 5}{x + 1}\right)}{\left(x + 1\right)^{2}}$$
The third derivative [src]
  /    5 + x\
6*|1 - -----|
  \    1 + x/
-------------
          3  
   (1 + x)   
$$\frac{6 \left(1 - \frac{x + 5}{x + 1}\right)}{\left(x + 1\right)^{3}}$$
The graph
Derivative of (x+5)/(x+1)