Mister Exam

Other calculators

Derivative of (x^2+3x+2)/(x-1)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 2          
x  + 3*x + 2
------------
   x - 1    
$$\frac{\left(x^{2} + 3 x\right) + 2}{x - 1}$$
(x^2 + 3*x + 2)/(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. Apply the power rule: goes to

      3. 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:

  2. Now simplify:


The answer is:

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