Mister Exam

Derivative of (2x+5)/(x-1)

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

The graph:

from to

Piecewise:

The solution

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