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

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

The graph:

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Piecewise:

The solution

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

        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       9*(x - 3)
-------- - ---------
       3           4
(x - 1)     (x - 1) 
$$- \frac{9 \left(x - 3\right)}{\left(x - 1\right)^{4}} + \frac{3}{\left(x - 1\right)^{3}}$$
The second derivative [src]
   /     2*(-3 + x)\
18*|-1 + ----------|
   \       -1 + x  /
--------------------
             4      
     (-1 + x)       
$$\frac{18 \left(\frac{2 \left(x - 3\right)}{x - 1} - 1\right)}{\left(x - 1\right)^{4}}$$
The third derivative [src]
   /    5*(-3 + x)\
36*|3 - ----------|
   \      -1 + x  /
-------------------
             5     
     (-1 + x)      
$$\frac{36 \left(- \frac{5 \left(x - 3\right)}{x - 1} + 3\right)}{\left(x - 1\right)^{5}}$$