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Derivative of:
Derivative of e^x*sinx
Derivative of -sin2x
Derivative of e^(2*x)*cos(x)
Derivative of e^(-5*x)
Graphing y =:
e^(-5*x)
Integral of d{x}:
e^(-5*x)
Limit of the function:
e^(-5*x)
Identical expressions
e^(- five *x)
e to the power of ( minus 5 multiply by x)
e to the power of ( minus five multiply by x)
e(-5*x)
e-5*x
e^(-5x)
e(-5x)
e-5x
e^-5x
Similar expressions
e^(5*x)

The derivative of the function/ e^(-5*x)

Derivative of e^(-5*x)

The solution

You have entered [src]

 -5*x
E

$$e^{- 5 x}$$

E^(-5*x)

Detail solution

Let $u = - 5 x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{d}{d x} \left(- 5 x\right)$ :
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: $-5$
The result of the chain rule is:

$- 5 e^{- 5 x}$

The answer is:

$- 5 e^{- 5 x}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

    -5*x
-5*e

$$- 5 e^{- 5 x}$$

Simplify

The second derivative [src]

    -5*x
25*e

$$25 e^{- 5 x}$$

Simplify

The third derivative [src]

      -5*x
-125*e

$$- 125 e^{- 5 x}$$

Simplify

The graph

Derivative of e^(-5*x)