Three times e to the power of three x is the derivative of e(3x). The equation is written as d/dx e(3x) = 3e in mathematical terms (3x).
The chain rule, in which e(3x) is written as f(g) and 3x is written as g, can be used to find the derivative of e(3x) (x). The formula f(g(x)) = f'(g(x))g’ is used to plug these values into (x). Three is the derivative of g(x), denoted as g'(x). Because the derivative of ex equals ex, the derivative of f(g), also written as f'(g), is e(3x). Three times e to the power of three x is the end result.