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

Derivative of (x-2)^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 - 2) 
--------
 x + 1  
$$\frac{\left(x - 2\right)^{2}}{x + 1}$$
(x - 2)^2/(x + 1)
Detail solution
  1. Apply the quotient rule, which is:

    and .

    To find :

    1. Let .

    2. Apply the power rule: goes to

    3. Then, apply the chain rule. Multiply by :

      1. Differentiate term by term:

        1. The derivative of the constant is zero.

        2. Apply the power rule: goes to

        The result is:

      The result of the chain rule 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
-4 + 2*x   (x - 2) 
-------- - --------
 x + 1            2
           (x + 1) 
$$- \frac{\left(x - 2\right)^{2}}{\left(x + 1\right)^{2}} + \frac{2 x - 4}{x + 1}$$
The second derivative [src]
  /            2             \
  |    (-2 + x)    2*(-2 + x)|
2*|1 + --------- - ----------|
  |            2     1 + x   |
  \     (1 + x)              /
------------------------------
            1 + x             
$$\frac{2 \left(\frac{\left(x - 2\right)^{2}}{\left(x + 1\right)^{2}} - \frac{2 \left(x - 2\right)}{x + 1} + 1\right)}{x + 1}$$
The third derivative [src]
  /             2             \
  |     (-2 + x)    2*(-2 + x)|
6*|-1 - --------- + ----------|
  |             2     1 + x   |
  \      (1 + x)              /
-------------------------------
                   2           
            (1 + x)            
$$\frac{6 \left(- \frac{\left(x - 2\right)^{2}}{\left(x + 1\right)^{2}} + \frac{2 \left(x - 2\right)}{x + 1} - 1\right)}{\left(x + 1\right)^{2}}$$
The graph
Derivative of (x-2)^2/(x+1)