What is the derivative of e^(2x) i am confused because the derivative e^x is e^x. but they say you need to use the chain rule. which is f'(g(x))*g'(x). i have used that on exponents but in this i just get, 2x * e^(2x-1) *e which is not the answer =/

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?