Mister Exam

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

Derivative of e^(-2x)

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^(-2x)