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Derivative of:
Derivative of 8^x
Derivative of e^(x*(-3))
Derivative of 1/(x+1)^2
Derivative of 1/(x+1)
Integral of d{x}:
1/(x+1)^2
How do you in partial fractions?:
1/(x+1)^2
Graphing y =:
1/(x+1)^2
Identical expressions
one /(x+ one)^ two
1 divide by (x plus 1) squared
one divide by (x plus one) to the power of two
1/(x+1)2
1/x+12
1/(x+1)²
1/(x+1) to the power of 2
1/x+1^2
1 divide by (x+1)^2
Similar expressions
1/(x-1)^2

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

Derivative of 1/(x+1)^2

The solution

You have entered [src]

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

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

1/((x + 1)^2)

Detail solution

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

$- \frac{2 x + 2}{\left(x + 1\right)^{4}}$
Now simplify:

$\frac{2}{\left(- x - 1\right)^{3}}$

The answer is:

$\frac{2}{\left(- x - 1\right)^{3}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

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

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

Simplify

The second derivative [src]

   6    
--------
       4
(1 + x)

$$\frac{6}{\left(x + 1\right)^{4}}$$

Simplify

The third derivative [src]

  -24   
--------
       5
(1 + x)

$$- \frac{24}{\left(x + 1\right)^{5}}$$

Simplify

The graph

Derivative of 1/(x+1)^2