1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Product rule

  1. Apr 21, 2010 #1
    How do I check [tex]\nabla[/tex] x (uv(hat)) = ([tex]\nabla[/tex]u) x v(hat) + u([tex]\nabla[/tex] x v(hat)).
     
  2. jcsd
  3. Apr 21, 2010 #2

    LCKurtz

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    Changing your notation a little, if f(x,y,z) is a scalar and

    V(x,y,z) = <u(x,y,z),v(x,y,z),w(x,y,z)> is a vector, to show

    [tex]\nabla \times f\vec V = \nabla f \times\vec V + f\nabla \times \vec V[/tex]

    just work both sides out in terms of components and compare. I don't think it matters whether V is a unit vector.
     
  4. Apr 21, 2010 #3

    gabbagabbahey

    User Avatar
    Homework Helper
    Gold Member

    The same way you prove every other vector calculus identity... express everything in terms of components, calculate the derivatives and simplify.

    Even if this isn't an assigned homework problem, it's still a homework type problem and you should follow the homework template.
     
  5. Apr 22, 2010 #4
    What if I wanted to use Cartesian coordinates, the definitions of the determinant, gradient and cross product of 2 vectors.
     
  6. Apr 22, 2010 #5

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    As a matter of fact, you pretty much have to use all of those. And work things out in terms of components of vectors, as others have said.

    Is this homework?
     
  7. Apr 22, 2010 #6
    Na. Studying for a test. It was a on a practice test.
     
  8. Apr 22, 2010 #7

    Redbelly98

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Moderator's note:

    I have moved this thread to the Homework & Coursework Questions area. We have guidelines on what belongs there, and this definitely qualifies.

    At this point, normal rules for Homework & Coursework apply. The OP should show an attempt at solving the problem before further help is given.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Product rule
  1. Product rule (Replies: 2)

  2. Product rule (Replies: 19)

  3. Product rule (Replies: 3)

  4. The Product Rule (Replies: 2)

  5. Product rule (Replies: 3)

Loading...