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Derivative of:
Derivative of x^x^x
Derivative of x^-6
Derivative of x^-11
Derivative of (x+5)/(x+1)
Identical expressions
- two /(x+ three)^ two
minus 2 divide by (x plus 3) squared
minus two divide by (x plus three) to the power of two
-2/(x+3)2
-2/x+32
-2/(x+3)²
-2/(x+3) to the power of 2
-2/x+3^2
-2 divide by (x+3)^2
Similar expressions
-2/(x-3)^2
2/(x+3)^2

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

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

The solution

You have entered [src]

  -2    
--------
       2
(x + 3)

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

-2/(x + 3)^2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = \left(x + 3\right)^{2}$ .
2. Apply the power rule: $\frac{1}{u}$ goes to $- \frac{1}{u^{2}}$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 3\right)^{2}$ :
  1. Let $u = x + 3$ .
  2. Apply the power rule: $u^{2}$ goes to $2 u$
  3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 3\right)$ :
    1. Differentiate $x + 3$ term by term:
      1. Apply the power rule: $x$ goes to $1$
      2. The derivative of the constant $3$ is zero.
      The result is: $1$
    The result of the chain rule is:
    
    $2 x + 6$
  The result of the chain rule is:
  
  $- \frac{2 x + 6}{\left(x + 3\right)^{4}}$
So, the result is: $\frac{2 \left(2 x + 6\right)}{\left(x + 3\right)^{4}}$
Now simplify:

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

The answer is:

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

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-2*(-6 - 2*x)
-------------
          4  
   (x + 3)

$$- \frac{2 \left(- 2 x - 6\right)}{\left(x + 3\right)^{4}}$$

Simplify

The second derivative [src]

  -12   
--------
       4
(3 + x)

$$- \frac{12}{\left(x + 3\right)^{4}}$$

Simplify

The third derivative [src]

   48   
--------
       5
(3 + x)

$$\frac{48}{\left(x + 3\right)^{5}}$$

Simplify