Mister Exam

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The derivative of the function/ e^(-4x)

Derivative of e^(-4x)

The solution

You have entered [src]

 -4*x
E

$$e^{- 4 x}$$

E^(-4*x)

Detail solution

Let $u = - 4 x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- 4 x\right)$ :
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: $-4$
The result of the chain rule is:

$- 4 e^{- 4 x}$

The answer is:

$- 4 e^{- 4 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -4*x
-4*e

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

Simplify

The second derivative [src]

    -4*x
16*e

$$16 e^{- 4 x}$$

Simplify

The third derivative [src]

     -4*x
-64*e

$$- 64 e^{- 4 x}$$

Simplify

The graph

Derivative of e^(-4x)