The derivative of e(3x) equals e to the power of three times three x. The equation can be written mathematically as d/dx e(3x) = 3e (3x).
Using the chain rule, one can determine the derivative of e(3x) by writing e(3x) as f(g) and 3x as g. (x). These numbers are entered into the equation f(g(x)) = f'(g(x))g’ (x). The derivative of g(x), g'(x), is equal to three. e(3x) is the derivative of f(g), also written as f'(g), as the derivative of ex equals ex. The outcome is three times e raised to the power of three x.