Mister Exam

Derivative of e^(a*x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src]
 a*x
E   
$$e^{a x}$$
E^(a*x)
Detail solution
  1. Let .

  2. The derivative of is itself.

  3. Then, apply the chain rule. Multiply by :

    1. The derivative of a constant times a function is the constant times the derivative of the function.

      1. Apply the power rule: goes to

      So, the result is:

    The result of the chain rule is:


The answer is:

The first derivative [src]
   a*x
a*e   
$$a e^{a x}$$
The second derivative [src]
 2  a*x
a *e   
$$a^{2} e^{a x}$$
The third derivative [src]
 3  a*x
a *e   
$$a^{3} e^{a x}$$