Derivative of f(z)=e^(-iz)

1. Let $u = - i z$.

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

3. Then, apply the chain rule. Multiply by $\frac{d}{d z} - i z$:

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

      1. Apply the power rule: $z$ goes to $1$

      So, the result is: $- i$

   The result of the chain rule is:

   $$- i e^{- i z}$$

4. Now simplify:

   $$- i e^{- i z}$$

The answer is:

$$- i e^{- i z}$$