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x/(x-2)
The derivative of the function/ x/(x-2)

Derivative of x/(x-2)

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

The graph:

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The solution

You have entered [src] 
  x  
-----
x - 2
xx−2\frac{x}{x - 2} 
x/(x - 2)
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)=xf{\left(x \right)} = x and g(x)=x−2g{\left(x \right)} = x - 2.

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

    1. Apply the power rule: xx goes to 11

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

    1. Differentiate x−2x - 2 term by term:

      1. The derivative of the constant −2-2 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    Now plug in to the quotient rule:

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

The answer is:

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

The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1        x    
----- - --------
x - 2          2
        (x - 2)
−x(x−2)2+1x−2- \frac{x}{\left(x - 2\right)^{2}} + \frac{1}{x - 2}
Simplify
The second derivative [src] 
  /       x   \
2*|-1 + ------|
  \     -2 + x/
---------------
           2   
   (-2 + x)
2(xx−2−1)(x−2)2\frac{2 \left(\frac{x}{x - 2} - 1\right)}{\left(x - 2\right)^{2}}
Simplify
The third derivative [src] 
  /      x   \
6*|1 - ------|
  \    -2 + x/
--------------
          3   
  (-2 + x)
6(−xx−2+1)(x−2)3\frac{6 \left(- \frac{x}{x - 2} + 1\right)}{\left(x - 2\right)^{3}}
Simplify
The graph
Derivative of x/(x-2)
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