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(x-2)/(x+3)
The derivative of the function/ (x-2)/(x+3)

Derivative of (x-2)/(x+3)

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

The graph:

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The solution

You have entered [src] 
x - 2
-----
x + 3
x−2x+3\frac{x - 2}{x + 3} 
(x - 2)/(x + 3)
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−2f{\left(x \right)} = x - 2 and g(x)=x+3g{\left(x \right)} = x + 3.

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

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

    1. Differentiate x+3x + 3 term by term:

      1. The derivative of the constant 33 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    Now plug in to the quotient rule:

    5(x+3)2\frac{5}{\left(x + 3\right)^{2}}

The answer is:

5(x+3)2\frac{5}{\left(x + 3\right)^{2}}

The graph
02468-8-6-4-2-10102000-1000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1      x - 2  
----- - --------
x + 3          2
        (x + 3)
−x−2(x+3)2+1x+3- \frac{x - 2}{\left(x + 3\right)^{2}} + \frac{1}{x + 3}
Simplify
The second derivative [src] 
  /     -2 + x\
2*|-1 + ------|
  \     3 + x /
---------------
           2   
    (3 + x)
2(x−2x+3−1)(x+3)2\frac{2 \left(\frac{x - 2}{x + 3} - 1\right)}{\left(x + 3\right)^{2}}
Simplify
The third derivative [src] 
  /    -2 + x\
6*|1 - ------|
  \    3 + x /
--------------
          3   
   (3 + x)
6(−x−2x+3+1)(x+3)3\frac{6 \left(- \frac{x - 2}{x + 3} + 1\right)}{\left(x + 3\right)^{3}}
Simplify
The graph
Derivative of (x-2)/(x+3)
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