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Derivative of:
Derivative of x-5
Derivative of 2*sinh(x)*cosh(x)
Derivative of x*ln(x)
Derivative of sqrt(x^2-1)
Integral of d{x}:
(1/2)^x
Limit of the function:
(1/2)^x
Graphing y =:
(1/2)^x
Identical expressions
(one / two)^x
(1 divide by 2) to the power of x
(one divide by two) to the power of x
(1/2)x
1/2x
1/2^x
(1 divide by 2)^x
Similar expressions
(1/(x*lnx))-(1/(2^x-1))

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

Derivative of (1/2)^x

The solution

You have entered [src]

 -x
2

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

(1/2)^x

Detail solution

Let $u = - x$ .
$\frac{d}{d u} 2^{u} = 2^{u} \log{\left(2 \right)}$
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:

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

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

The graph

Derivative of (1/2)^x