Question

How do you find the derivative of `y = 2e^x`?

Answer 1

You're going to hate me, but you have the derivative already.

The derivative of `e^x` is itself, and constants can be floated out of the derivative. So, what you have is:

`color(blue)(d/(dx)[2e^(x)])`

`= 2d/(dx)[e^x]`

`= color(blue)(2e^x)`

You don't do anything with the chain rule, because `d/(dx)[e^u] = e^u ((du)/(dx))`, but since `u(x) = x`, `(du)/(dx) = 1`, and therefore, `d/(dx)[e^x] = e^x * 1 = e^x`.