## anonymous one year ago 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

1. IrishBoy123

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

2. IrishBoy123

make any sense?

3. IrishBoy123

or see it as $$y = e^u, \ u = f(x)$$ then chain rule $$\large \frac{dy}{dx} = \frac {dy}{du}\frac{du}{dx}$$

4. anonymous

ok I see it. thanks again