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

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

irishboy123 · Answer

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

irishboy123 · Answer

make any sense?

irishboy123 · Answer

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

anonymous · Answer

ok I see it. thanks again