Mister Exam

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

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
x - 2
-----
x - 3
$$\frac{x - 2}{x - 3}$$
(x - 2)/(x - 3)
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 - 2  
----- - --------
x - 3          2
        (x - 3) 
$$\frac{1}{x - 3} - \frac{x - 2}{\left(x - 3\right)^{2}}$$
The second derivative [src]
  /     -2 + x\
2*|-1 + ------|
  \     -3 + x/
---------------
           2   
   (-3 + x)    
$$\frac{2 \left(-1 + \frac{x - 2}{x - 3}\right)}{\left(x - 3\right)^{2}}$$
The third derivative [src]
  /    -2 + x\
6*|1 - ------|
  \    -3 + x/
--------------
          3   
  (-3 + x)    
$$\frac{6 \left(1 - \frac{x - 2}{x - 3}\right)}{\left(x - 3\right)^{3}}$$
3-я производная [src]
  /    -2 + x\
6*|1 - ------|
  \    -3 + x/
--------------
          3   
  (-3 + x)    
$$\frac{6 \left(1 - \frac{x - 2}{x - 3}\right)}{\left(x - 3\right)^{3}}$$