Question

What is the `100`th derivative of `2e^x`?

Answer 1

Well, you should memorize that the derivative of `e^x` is `e^x`. Therefore, `(d^n)/(dx^n)[e^x] = f^((n))(x) = e^x`.

The constant floats out front, so

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

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

`= 2e^x`

Since we just proved it in general, what does that tell you about the `100`th derivative?