Mister Exam

Lang:

Other calculators

How to use it?
Derivative of:
Derivative of x^(4/5)
Derivative of ln(1-x)
Derivative of log(x^2+5)
Derivative of e^(-2*x)
Integral of d{x}:
e^(-2*x)
Limit of the function:
e^(-2*x)
Identical expressions
e^(- two *x)
e to the power of ( minus 2 multiply by x)
e to the power of ( minus two multiply by x)
e(-2*x)
e-2*x
e^(-2x)
e(-2x)
e-2x
e^-2x
Similar expressions
e^(2*x)
(√x^3+4)*e^(-2x)
y=-e^(-2x)*(-sinx+2*cosx)
2e^(-2x)+√x
y'''=e^(-2x)
y=x*e^(-2x)

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

Derivative of e^(-2*x)

The solution

You have entered [src]

 -2*x
E

$$e^{- 2 x}$$

E^(-2*x)

Detail solution

Let $u = - 2 x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- 2 x\right)$ :
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: $-2$
The result of the chain rule is:

$- 2 e^{- 2 x}$

The answer is:

$- 2 e^{- 2 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -2*x
-2*e

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

Simplify

The second derivative [src]

   -2*x
4*e

$$4 e^{- 2 x}$$

Simplify

The third derivative [src]

    -2*x
-8*e

$$- 8 e^{- 2 x}$$

Simplify

The graph

Derivative of e^(-2*x)