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

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

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

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The solution

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

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

    1. Differentiate x−3x - 3 term by term:

      1. The derivative of the constant −3-3 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+2x + 2 term by term:

      1. The derivative of the constant 22 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    Now plug in to the quotient rule:

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

The answer is:

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