Derivative of e^(ax)

1. Let $u = a x$.

2. The derivative of $e^{u}$ is itself.

3. 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:

   $$a e^{a x}$$

The answer is:

$$a e^{a x}$$