A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 4 years ago
Prove the following vector identities letting:
V = u i + v j + w k and ∇= ∂╱∂x i + ∂╱∂y j + ∂╱∂z k that:
∇∙(fV̅) = f (∇∙V̅) + V̅ ∙∇f
anonymous
 4 years ago
Prove the following vector identities letting: V = u i + v j + w k and ∇= ∂╱∂x i + ∂╱∂y j + ∂╱∂z k that: ∇∙(fV̅) = f (∇∙V̅) + V̅ ∙∇f

This Question is Closed

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I am aware. I meant write down what it actually is.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0f (u)i + f(v) j + f(w)k

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0f is multiply u, v, and w, right?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0So what's the divergence of that?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0∂╱∂x i + ∂╱∂y j + ∂╱∂z k

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0No, what is the divergence of the expression you wrote for fV ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0i'm not quite following what your asking me

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[f\vec{V} = fu\vec{i} + fv\vec{j} + fw\vec{k} \] what is \[\vec{\nabla} \cdot (f\vec{V}) \] ?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0d f(u)/dx i + d f(v)/dy j + d f(w)/dz k

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0the i, j, and k are gone.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Okay, so expand that out.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0so just d f(u)/dx + d f(v)/dy + d f(w)/dz

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That's right. Now show that that equals the identity that you were given above.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well the right hand side of the equation is where the problems start

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[ \frac{\partial (fu)}{\partial x} = \frac{ \partial f}{\partial x} u + f\frac{\partial u}{\partial x}\] etc....

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0those are equal what u just wrote above?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0That's only the first term...

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0oh i think i just clicked what ur saying

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay..so the entire left side is now expanded

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0okay....i think i see where this is going now

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0if i expand the right side it's gonna come out the same way huh?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Yeah but it would probably be better if you just grouped the terms on the left. \[f \frac{\partial u}{\partial x} + f\frac{\partial v}{\partial y} + f\frac{\partial w}{\partial z} = f(\vec{\nabla} \cdot \vec{V})\] and so forth..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0thank you soo soo much
Ask your own question
Sign UpFind more explanations on OpenStudy
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.