Mister Exam

Derivative of (2x+1)/(x+2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
2*x + 1
-------
 x + 2 
$$\frac{2 x + 1}{x + 2}$$
(2*x + 1)/(x + 2)
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. The derivative of a constant times a function is the constant times the derivative of the function.

        1. Apply the power rule: goes to

        So, the result is:

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