Question

lim x^3 * e^(-x/2)
x→∞
I have the answer to the problem which is 0 but, I don't understand the derivative of e^(-x/2). can someone explain how that derivative works? I just need to know the derivative, not the answer to the whole problem

Answer 1

\[ \left( e^{f(x)}\right)' = f'(x) e^{f(x)}\]

Answer 2

make any sense?

Answer 3

or see it as \(y = e^u, \ u = f(x)\)
then chain rule

\(\large \frac{dy}{dx} = \frac {dy}{du}\frac{du}{dx}\)

Answer 4

ok I see it. thanks again