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(x-3)^2/(4(x-1))

Derivative of (x-3)^2/(4(x-1))

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

The graph:

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Piecewise:

The solution

You have entered [src]
        2
 (x - 3) 
---------
4*(x - 1)
$$\frac{\left(x - 3\right)^{2}}{4 \left(x - 1\right)}$$
  /        2\
d | (x - 3) |
--|---------|
dx\4*(x - 1)/
$$\frac{d}{d x} \frac{\left(x - 3\right)^{2}}{4 \left(x - 1\right)}$$
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. 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:

    Now plug in to the quotient rule:

  2. Now simplify:


The answer is:

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