Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
JingleBells
Group Title
The graph of the function y=e^(x^2/2) isn't the same as the graph of the function y=e^(x) is it because that the first expression wants a positive value of all x?
And does anyone know d/dx (x^21)e^(x^2/2)?
 2 years ago
 2 years ago
JingleBells Group Title
The graph of the function y=e^(x^2/2) isn't the same as the graph of the function y=e^(x) is it because that the first expression wants a positive value of all x? And does anyone know d/dx (x^21)e^(x^2/2)?
 2 years ago
 2 years ago

This Question is Closed

student92 Group TitleBest ResponseYou've already chosen the best response.0
Both \[f(x)=e^{(x^2/2)}\]\[y=e^{x}\]may have negative value for x. Following links provide the graph of each function. f(x) > http://www.wolframalpha.com/input/?i=y%3De^%28x^2%2F2%29 g(x) > http://www.wolframalpha.com/input/?i=y%3De^%28x%29 Note something: 1) ^2 cause concave up. 2)  sign cause mirror image of the + graphs. Hence g(x) is a mirror image of e^x , whereas f(x) has a concave, but it is down due to the negative sign.
 2 years ago

student92 Group TitleBest ResponseYou've already chosen the best response.0
On the second question First of all, multiply/rearrange the function. \[f(x)=(x^21)(e^{x^2/2})=x^2 e^{x^2/2}e^{x^2/2}\]Next, we use chain rule.\[f'(x)=2xe^{x^2/2}+x^2(2x/2)e^{x^2/2}+()(2x/2)e^{x^2/2}\]\[f'(x)=2xe^{x^2/2}x^3e^{x^2/2}+xe^{x^2/2}\]\[f'(x)=e^{x^2/2}(2xx^3+x)\]\[f'(x)=e^{x^2/2}(3xx^3)\]
 2 years ago

student92 Group TitleBest ResponseYou've already chosen the best response.0
P.S. g(x) I mentioned on the first response is y=e^x
 2 years ago

JingleBells Group TitleBest ResponseYou've already chosen the best response.0
This is what I meant and I graphed and expected to see the same graph...
 2 years ago

student92 Group TitleBest ResponseYou've already chosen the best response.0
\[\frac{1}{\sqrt{e^{x^2}}} \neq \frac{1}{e^x}\] I think you mistaken \[\frac{1}{\sqrt{e^{x^2}}} \text{as} \frac{1}{\sqrt{e^{2x}}}\]See? say for example e=2.7 and let x=2. If you subtitle those values to what you meant before, the left hand side (LHS) will be diferrent to right hand side (RHS).
 2 years ago

JingleBells Group TitleBest ResponseYou've already chosen the best response.0
of course haha it's been a long day thanks! I was just starting to freak out...
 2 years ago

student92 Group TitleBest ResponseYou've already chosen the best response.0
LOL. You just need to take a fresh air. Observe that the ^2 here is for x only; not (e^x) altogether. \[e^{(x^2)} \neq (e^x)^2 \]
 2 years ago

JingleBells Group TitleBest ResponseYou've already chosen the best response.0
Good idea! Going for a run and pump some more blood into my head. Thanks!
 2 years ago

opendiscuss Group TitleBest ResponseYou've already chosen the best response.0
student 92.... i do not think e(x^2)≠(e^x)^2 They are both equal....
 2 years ago

student92 Group TitleBest ResponseYou've already chosen the best response.0
let just say \( x=1 \). \[e(x^2)=e(1^2)=e \]\[(e^x)^2=(e^1)^2=e^2 \]Are they still the same?
 2 years ago
See more questions >>>
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.