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

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

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

The graph:

from to

Piecewise:

The solution

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

      The result of the chain rule is:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
    3        (-4 - 8*x)*(3*x - 1)
---------- + --------------------
         2                 4     
(2*x + 1)         (2*x + 1)      
$$\frac{\left(- 8 x - 4\right) \left(3 x - 1\right)}{\left(2 x + 1\right)^{4}} + \frac{3}{\left(2 x + 1\right)^{2}}$$
The second derivative [src]
   /     -1 + 3*x\
24*|-1 + --------|
   \     1 + 2*x /
------------------
             3    
    (1 + 2*x)     
$$\frac{24 \left(-1 + \frac{3 x - 1}{2 x + 1}\right)}{\left(2 x + 1\right)^{3}}$$
The third derivative [src]
   /    8*(-1 + 3*x)\
24*|9 - ------------|
   \      1 + 2*x   /
---------------------
               4     
      (1 + 2*x)      
$$\frac{24 \left(9 - \frac{8 \left(3 x - 1\right)}{2 x + 1}\right)}{\left(2 x + 1\right)^{4}}$$
The graph
Derivative of (3x-1)/(2x+1)^2