Mister Exam

Derivative of (x-3)/(x+2)

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

The graph:

from to

Piecewise:

The solution

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