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(2*x-9)/(x-5)
The derivative of the function/ (2*x-9)/(x-5)

Derivative of (2*x-9)/(x-5)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
2*x - 9
-------
 x - 5
2x−9x−5\frac{2 x - 9}{x - 5} 
(2*x - 9)/(x - 5)
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)=2x−9f{\left(x \right)} = 2 x - 9 and g(x)=x−5g{\left(x \right)} = x - 5.

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

    1. Differentiate 2x−92 x - 9 term by term:

      1. The derivative of the constant −9-9 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: xx goes to 11

        So, the result is: 22

      The result is: 22

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

    1. Differentiate x−5x - 5 term by term:

      1. The derivative of the constant −5-5 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    Now plug in to the quotient rule:

    −1(x−5)2- \frac{1}{\left(x - 5\right)^{2}}

The answer is:

−1(x−5)2- \frac{1}{\left(x - 5\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] 
  2     2*x - 9 
----- - --------
x - 5          2
        (x - 5)
2x−5−2x−9(x−5)2\frac{2}{x - 5} - \frac{2 x - 9}{\left(x - 5\right)^{2}}
Simplify
The second derivative [src] 
  /     -9 + 2*x\
2*|-2 + --------|
  \      -5 + x /
-----------------
            2    
    (-5 + x)
2(−2+2x−9x−5)(x−5)2\frac{2 \left(-2 + \frac{2 x - 9}{x - 5}\right)}{\left(x - 5\right)^{2}}
Simplify
The third derivative [src] 
  /    -9 + 2*x\
6*|2 - --------|
  \     -5 + x /
----------------
           3    
   (-5 + x)
6(2−2x−9x−5)(x−5)3\frac{6 \left(2 - \frac{2 x - 9}{x - 5}\right)}{\left(x - 5\right)^{3}}
Simplify
The graph
Derivative of (2*x-9)/(x-5)
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