Differentiate: x*e^((-x^2)/2)

Please show work. Kind regards...

Question

Differentiate: x*e^((-x^2)/2)

Please show work. Kind regards...

experimentx · Answer

anonymous · Answer

yeah, wolfram alpha is good but I do not always trust it . It is great to check your work though. Thanks for your help experimentX

helder_edwin · Answer

you have the product of two functions $f(x)=x$ and $g(x)=e^{-x^2/2}$

anonymous · Answer

okay, should I use both the product rule and chain rule

helder_edwin · Answer

yes

helder_edwin · Answer

so u would have
\[ y'=e^{-x^2/2}+xe^{-x^2/2}(-x)

anonymous · Answer

okay

helder_edwin · Answer

finally u have
$$ y'=e^{-x^2/2}(1-x^2) $$

anonymous · Answer

is that after you have done the chain rule.?

helder_edwin · Answer

i applied the chain rule to the exponential rule

helder_edwin · Answer

sorry exponential functiom

anonymous · Answer

yes

helder_edwin · Answer

i have to go
good luck

anonymous · Answer

thank you very much
You are a great help

anonymous · Answer

experimentX - The wolfram answer was correct as well. I just needed a verified reply from a human. :)