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

Derivative of e^(-4x)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
 -4*x
E
e−4xe^{- 4 x} 
E^(-4*x)
Detail solution

  1. Let u=−4xu = - 4 x.

  2. The derivative of eue^{u} is itself.

  3. Then, apply the chain rule. Multiply by ddx(−4x)\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: xx goes to 11

      So, the result is: −4-4

    The result of the chain rule is:

    −4e−4x- 4 e^{- 4 x}

The answer is:

−4e−4x- 4 e^{- 4 x}

The graph
02468-8-6-4-2-1010-500000000000000000500000000000000000
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    -4*x
-4*e
−4e−4x- 4 e^{- 4 x}
Simplify
The second derivative [src] 
    -4*x
16*e
16e−4x16 e^{- 4 x}
Simplify
The third derivative [src] 
     -4*x
-64*e
−64e−4x- 64 e^{- 4 x}
Simplify
The graph
Derivative of e^(-4x)
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