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Derivative of:
Derivative of x^2+cos(x)
Derivative of x*sin(3*x)
Derivative of cos(3)^(2)*x-sin(3)^(2)*x
Derivative of (3*x+1)^2
Graphing y =:
(1/2)^x+1
Identical expressions
(one / two)^x+ one
(1 divide by 2) to the power of x plus 1
(one divide by two) to the power of x plus one
(1/2)x+1
1/2x+1
1/2^x+1
(1 divide by 2)^x+1
Similar expressions
(1/2)^x-1

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

Derivative of (1/2)^x+1

The solution

You have entered [src]

 -x    
2   + 1

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

(1/2)^x + 1

Detail solution

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

The answer is:

$- 2^{- x} \log{\left(2 \right)}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  -x       
-2  *log(2)

$$- 2^{- x} \log{\left(2 \right)}$$

Simplify

The second derivative [src]

 -x    2   
2  *log (2)

$$2^{- x} \log{\left(2 \right)}^{2}$$

Simplify

The third derivative [src]

  -x    3   
-2  *log (2)

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

Simplify

3-я производная [src]

  -x    3   
-2  *log (2)

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

Simplify