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The derivative of the function/ 1/(x^2+2x+3)

Derivative of 1/(x^2+2x+3)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     1      
------------
 2          
x  + 2*x + 3
$$\frac{1}{\left(x^{2} + 2 x\right) + 3}$$ 
1/(x^2 + 2*x + 3)
Detail solution

  1. Let .

  2. Apply the power rule: goes to

  3. Then, apply the chain rule. Multiply by :

    1. Differentiate term by term:

      1. Differentiate term by term:

        1. Apply the power rule: goes to

        2. The derivative of a constant times a function is the constant times the derivative of the function.

          1. Apply the power rule: goes to

          So, the result is:

        The result is:

      2. The derivative of the constant is zero.

      The result is:

    The result of the chain rule is:

  4. Now simplify:

The answer is:

The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    -2 - 2*x   
---------------
              2
/ 2          \ 
\x  + 2*x + 3/
$$\frac{- 2 x - 2}{\left(\left(x^{2} + 2 x\right) + 3\right)^{2}}$$
Simplify
The second derivative [src] 
  /               2 \
  |      4*(1 + x)  |
2*|-1 + ------------|
  |          2      |
  \     3 + x  + 2*x/
---------------------
                 2   
   /     2      \    
   \3 + x  + 2*x/
$$\frac{2 \left(\frac{4 \left(x + 1\right)^{2}}{x^{2} + 2 x + 3} - 1\right)}{\left(x^{2} + 2 x + 3\right)^{2}}$$
Simplify
The third derivative [src] 
           /              2 \
           |     2*(1 + x)  |
24*(1 + x)*|1 - ------------|
           |         2      |
           \    3 + x  + 2*x/
-----------------------------
                     3       
       /     2      \        
       \3 + x  + 2*x/
$$\frac{24 \left(x + 1\right) \left(- \frac{2 \left(x + 1\right)^{2}}{x^{2} + 2 x + 3} + 1\right)}{\left(x^{2} + 2 x + 3\right)^{3}}$$
Simplify
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