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(x+5)/(x-1)
The derivative of the function/ (x+5)/(x-1)

Derivative of (x+5)/(x-1)

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

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The solution

You have entered [src] 
x + 5
-----
x - 1
x+5x−1\frac{x + 5}{x - 1} 
(x + 5)/(x - 1)
Detail solution

  1. Apply the quotient rule, which is:

    ddxf(x)g(x)=−f(x)ddxg(x)+g(x)ddxf(x)g2(x)\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}

    f(x)=x+5f{\left(x \right)} = x + 5 and g(x)=x−1g{\left(x \right)} = x - 1.

    To find ddxf(x)\frac{d}{d x} f{\left(x \right)}:

    1. Differentiate x+5x + 5 term by term:

      1. The derivative of the constant 55 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    To find ddxg(x)\frac{d}{d x} g{\left(x \right)}:

    1. Differentiate x−1x - 1 term by term:

      1. The derivative of the constant −1-1 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    Now plug in to the quotient rule:

    −6(x−1)2- \frac{6}{\left(x - 1\right)^{2}}

The answer is:

−6(x−1)2- \frac{6}{\left(x - 1\right)^{2}}

The graph
02468-8-6-4-2-1010-10001000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1      x + 5  
----- - --------
x - 1          2
        (x - 1)
1x−1−x+5(x−1)2\frac{1}{x - 1} - \frac{x + 5}{\left(x - 1\right)^{2}}
Simplify
The second derivative [src] 
  /     5 + x \
2*|-1 + ------|
  \     -1 + x/
---------------
           2   
   (-1 + x)
2(−1+x+5x−1)(x−1)2\frac{2 \left(-1 + \frac{x + 5}{x - 1}\right)}{\left(x - 1\right)^{2}}
Simplify
The third derivative [src] 
  /    5 + x \
6*|1 - ------|
  \    -1 + x/
--------------
          3   
  (-1 + x)
6(1−x+5x−1)(x−1)3\frac{6 \left(1 - \frac{x + 5}{x - 1}\right)}{\left(x - 1\right)^{3}}
Simplify
The graph
Derivative of (x+5)/(x-1)
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