Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of (x+5)/(x+1)
Derivative of -x/2
Derivative of sin(4x)
Derivative of x*2^x
Limit of the function:
e^(-x)/2
Identical expressions
e^(-x)/ two
e to the power of ( minus x) divide by 2
e to the power of ( minus x) divide by two
e(-x)/2
e-x/2
e^-x/2
e^(-x) divide by 2
Similar expressions
e^(x)/2

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

Derivative of e^(-x)/2

The solution

You have entered [src]

 -x
E  
---
 2

$$\frac{e^{- x}}{2}$$

E^(-x)/2

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Let $u = - x$ .
2. The derivative of $e^{u}$ is itself.
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:
  
  $- e^{- x}$
So, the result is: $- \frac{e^{- x}}{2}$

The answer is:

$- \frac{e^{- x}}{2}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

  -x 
-e   
-----
  2

$$- \frac{e^{- x}}{2}$$

Simplify

The second derivative [src]

 -x
e  
---
 2

$$\frac{e^{- x}}{2}$$

Simplify

The third derivative [src]

  -x 
-e   
-----
  2

$$- \frac{e^{- x}}{2}$$

Simplify

The graph

Derivative of e^(-x)/2