Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of 2/x²
Derivative of 2/(x+1)^2
Derivative of 2^(3*x)/3^(2*x)
Derivative of -1/3
Integral of d{x}:
2/(x+1)^2
How do you in partial fractions?:
2/(x+1)^2
Graphing y =:
2/(x+1)^2
Identical expressions
two /(x+ one)^ two
2 divide by (x plus 1) squared
two divide by (x plus one) to the power of two
2/(x+1)2
2/x+12
2/(x+1)²
2/(x+1) to the power of 2
2/x+1^2
2 divide by (x+1)^2
Similar expressions
2/(x-1)^2

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

Derivative of 2/(x+1)^2

The solution

You have entered [src]

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

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

2/(x + 1)^2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \left(x + 1\right)^{2}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. 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:
  
  $- \frac{2 x + 2}{\left(x + 1\right)^{4}}$
So, the result is: $- \frac{2 \left(2 x + 2\right)}{\left(x + 1\right)^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

2*(-2 - 2*x)
------------
         4  
  (x + 1)

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

Simplify

The second derivative [src]

   12   
--------
       4
(1 + x)

$$\frac{12}{\left(x + 1\right)^{4}}$$

Simplify

The third derivative [src]

  -48   
--------
       5
(1 + x)

$$- \frac{48}{\left(x + 1\right)^{5}}$$

Simplify

The graph

Derivative of 2/(x+1)^2