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Derivative of:
Derivative of x^2*e^2
Derivative of 3^-x
Derivative of e^(x*(-4))
Derivative of (3x-5)^3
Integral of d{x}:
e^(x*(-4))
Identical expressions
e^(x*(- four))
e to the power of (x multiply by ( minus 4))
e to the power of (x multiply by ( minus four))
e(x*(-4))
ex*-4
e^(x(-4))
e(x(-4))
ex-4
e^x-4
Similar expressions
e^(x*(4))

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

Derivative of e^(x*(-4))

The solution

You have entered [src]

 x*(-4)
E

$$e^{\left(-4\right) x}$$

E^(x*(-4))

Detail solution

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

$- 4 e^{\left(-4\right) x}$
Now simplify:

$- 4 e^{- 4 x}$

The answer is:

$- 4 e^{- 4 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    x*(-4)
-4*e

$$- 4 e^{\left(-4\right) x}$$

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^(x*(-4))