The derivative of e^(g(x)) can be determined using the chain rule. The chain rule states that if we have a composite function, f(g(x)), where f is a differentiable function and g is a differentiable function, then the derivative of f(g(x)) is f'(g(x)) * g'(x).

In this case, f(x) = e^x and g(x) = g(x), so we have:

d/dx [e^(g(x))] = d/dx [e^x] * d/dx [g(x)]

= e^(g(x)) * g'(x)

So the derivative of e^(g(x)) is e^(g(x)) * g'(x).
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