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Derivative of:
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Integral of d{x}:
1/(x+2)^2
How do you in partial fractions?:
1/(x+2)^2
Graphing y =:
1/(x+2)^2
Identical expressions
one /(x+ two)^ two
1 divide by (x plus 2) squared
one divide by (x plus two) to the power of two
1/(x+2)2
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1/(x+2) to the power of 2
1/x+2^2
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Similar expressions
1/(x-2)^2

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

Derivative of 1/(x+2)^2

The solution

You have entered [src]

   1    
--------
       2
(x + 2)

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

1/((x + 2)^2)

Detail solution

Let $u = \left(x + 2\right)^{2}$ .
Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 2\right)^{2}$ :
1. Let $u = x + 2$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 2\right)$ :
  1. Differentiate $x + 2$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $2$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $2 x + 4$
The result of the chain rule is:

$- \frac{2 x + 4}{\left(x + 2\right)^{4}}$
Now simplify:

$\frac{2}{\left(- x - 2\right)^{3}}$

The answer is:

$\frac{2}{\left(- x - 2\right)^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

     -4 - 2*x    
-----------------
       2        2
(x + 2) *(x + 2)

$$\frac{- 2 x - 4}{\left(x + 2\right)^{2} \left(x + 2\right)^{2}}$$

Simplify

The second derivative [src]

   6    
--------
       4
(2 + x)

$$\frac{6}{\left(x + 2\right)^{4}}$$

Simplify

The third derivative [src]

  -24   
--------
       5
(2 + x)

$$- \frac{24}{\left(x + 2\right)^{5}}$$

Simplify

The graph

Derivative of 1/(x+2)^2