Final answer:
The derivative of z = e^(8x) is 8e^(8x), found using the chain rule.
Step-by-step explanation:
The derivative of z = e^(8x) with respect to x is found using the chain rule of differentiation. The chain rule states that the derivative of a composition of functions is the derivative of the outer function evaluated at the inner function times the derivative of the inner function. In this case, the outer function is e^u where u = 8x. The derivative of e^u with respect to u is itself, e^u, and the derivative of u = 8x with respect to x is 8. Applying the chain rule gives us: