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Derivative of:
Derivative of e^2*x
Derivative of x^sin(x)
Derivative of sqrt(x^2+1)
Derivative of 4/x^2
Graphing y =:
(x+4)^2+2
Identical expressions
(x+ four)^ two + two
(x plus 4) squared plus 2
(x plus four) to the power of two plus two
(x+4)2+2
x+42+2
(x+4)²+2
(x+4) to the power of 2+2
x+4^2+2
Similar expressions
(x+4)^2-2
(x-4)^2+2

The derivative of the function/ (x+4)^2+2

Derivative of (x+4)^2+2

The solution

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       2    
(x + 4)  + 2

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

(x + 4)^2 + 2

Detail solution

Differentiate $\left(x + 4\right)^{2} + 2$ term by term:
1. Let $u = x + 4$ .
2. Apply the power rule: $u^{2}$ goes to $2 u$
3. Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(x + 4\right)$ :
  1. Differentiate $x + 4$ term by term:
    1. Apply the power rule: $x$ goes to $1$
    2. The derivative of the constant $4$ is zero.
    The result is: $1$
  The result of the chain rule is:
  
  $2 x + 8$
4. The derivative of the constant $2$ is zero.
The result is: $2 x + 8$

The answer is:

$2 x + 8$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

8 + 2*x

$$2 x + 8$$

Simplify

The second derivative [src]

$$2$$

Simplify

The third derivative [src]

$$0$$

Simplify