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

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

The graph:

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The solution

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

    ; to find :

    1. Differentiate term by term:

      1. Apply the power rule: goes to

      2. The derivative of the constant is zero.

      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. Apply the power rule: goes to

        2. The derivative of the constant is zero.

        The result is:

      The result of the chain rule is:

    The result is:

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
       2/3    2*(x + 1) 
(x - 1)    + -----------
               3 _______
             3*\/ x - 1 
$$\left(x - 1\right)^{\frac{2}{3}} + \frac{2 \left(x + 1\right)}{3 \sqrt[3]{x - 1}}$$
The second derivative [src]
  /    1 + x \
2*|6 - ------|
  \    -1 + x/
--------------
   3 ________ 
 9*\/ -1 + x  
$$\frac{2 \left(6 - \frac{x + 1}{x - 1}\right)}{9 \sqrt[3]{x - 1}}$$
The third derivative [src]
  /     4*(1 + x)\
2*|-9 + ---------|
  \       -1 + x /
------------------
             4/3  
  27*(-1 + x)     
$$\frac{2 \left(-9 + \frac{4 \left(x + 1\right)}{x - 1}\right)}{27 \left(x - 1\right)^{\frac{4}{3}}}$$