Mister Exam

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The derivative of the function/ exp(-ax)

Derivative of exp(-ax)

The solution

You have entered [src]

 -a*x
e

$$e^{- a x}$$

exp((-a)*x)

Detail solution

Let $u = - a x$ .
The derivative of $e^{u}$ is itself.
Then, apply the chain rule. Multiply by $\frac{\partial}{\partial x} - a x$ :
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: $- a$
The result of the chain rule is:

$- a e^{- a x}$
Now simplify:

$- a e^{- a x}$

The answer is:

$- a e^{- a x}$

The first derivative [src]

    -a*x
-a*e

$$- a e^{- a x}$$

Simplify

The second derivative [src]

 2  -a*x
a *e

$$a^{2} e^{- a x}$$

Simplify

The third derivative [src]

  3  -a*x
-a *e

$$- a^{3} e^{- a x}$$

Simplify