Mister Exam

Derivative of x/(x-2)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
  x  
-----
x - 2
$$\frac{x}{x - 2}$$
x/(x - 2)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Apply the power rule: goes to

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