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(x+3)/(x+1)
The derivative of the function/ (x+3)/(x+1)

Derivative of (x+3)/(x+1)

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

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The solution

You have entered [src] 
x + 3
-----
x + 1
x+3x+1\frac{x + 3}{x + 1} 
d /x + 3\
--|-----|
dx\x + 1/
ddxx+3x+1\frac{d}{d x} \frac{x + 3}{x + 1}
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+1g{\left(x \right)} = x + 1.

    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 33 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 11 is zero.

      2. Apply the power rule: xx goes to 11

      The result is: 11

    Now plug in to the quotient rule:

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

The answer is:

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

The graph
02468-8-6-4-2-1010-250250
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1      x + 3  
----- - --------
x + 1          2
        (x + 1)
1x+1−x+3(x+1)2\frac{1}{x + 1} - \frac{x + 3}{\left(x + 1\right)^{2}}
Simplify
The second derivative [src] 
  /     3 + x\
2*|-1 + -----|
  \     1 + x/
--------------
          2   
   (1 + x)
2(−1+x+3x+1)(x+1)2\frac{2 \left(-1 + \frac{x + 3}{x + 1}\right)}{\left(x + 1\right)^{2}}
Simplify
The third derivative [src] 
  /    3 + x\
6*|1 - -----|
  \    1 + x/
-------------
          3  
   (1 + x)
6⋅(1−x+3x+1)(x+1)3\frac{6 \cdot \left(1 - \frac{x + 3}{x + 1}\right)}{\left(x + 1\right)^{3}}
Simplify
The graph
Derivative of (x+3)/(x+1)
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