Maybe I'm not fully understanding the chain rule, but anyways I'll give my argument. At any given point the function e^(2x) is squared the original function of e^x. So why is the derivative of e^(2x), two times the squared the derivative of the e^x, and not just squared the derivative of the latter function? Hope you understand what I'm saying. If you don't understand, let me know I'll elucidate. Also when you try to explain, please do not just regurgitate the definition of chain rule, but try to explain the intuition behind this.