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Derivative of:
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Derivative of a^2
Graphing y =:
1/(x+1)^3
Integral of d{x}:
1/(x+1)^3
Identical expressions
one /(x+ one)^ three
1 divide by (x plus 1) cubed
one divide by (x plus one) to the power of three
1/(x+1)3
1/x+13
1/(x+1)³
1/(x+1) to the power of 3
1/x+1^3
1 divide by (x+1)^3
Similar expressions
1/(x-1)^3

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

Derivative of 1/(x+1)^3

The solution

You have entered [src]

   1    
--------
       3
(x + 1)

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

1/((x + 1)^3)

Detail solution

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

$- \frac{3}{\left(x + 1\right)^{4}}$
Now simplify:

$- \frac{3}{\left(x + 1\right)^{4}}$

The answer is:

$- \frac{3}{\left(x + 1\right)^{4}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

      -3        
----------------
               3
(x + 1)*(x + 1)

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

Simplify

The second derivative [src]

   12   
--------
       5
(1 + x)

$$\frac{12}{\left(x + 1\right)^{5}}$$

Simplify

The third derivative [src]

  -60   
--------
       6
(1 + x)

$$- \frac{60}{\left(x + 1\right)^{6}}$$

Simplify

The graph

Derivative of 1/(x+1)^3