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(x^2-x+2)/(x+1)

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