What is the derivative of e^(2x)?
is it necessary to use the chain rule: f'(g(x))*g'(x)?

The derivative of e^(2x) is d/dx( e^(2x)) = e^(2x). d/dx (2x) = e^(2x).2 = 2e^(2x) . Yes, it is necessary to use the chain rule. Because withour chain rule the differentiation will be incomplete. Thsu, the derivtive of e^(2x) is 2e^(2x).