The derivative of e^(3x) is equal to three times e to the power of three x. In mathematical terms, the equation can be expressed as d/dx e^(3x) = 3e^(3x).
The derivative of e^(3x) can be found using the chain rule, in which e^(3x) is written as f(g) and 3x is written as g(x). These values are plugged into the formula f(g(x)) = f'(g(x))g'(x). The derivative of g(x), written as g'(x), is three. The derivative of f(g), also written as f'(g), is e^(3x) because the derivative of e^x is equal to e^x. The resulting product is three times e to the power of three x.