Results 1 to 3 of 3

Math Help - Derivative of a Vector Proof

  1. #1
    Junior Member
    Joined
    Apr 2010
    From
    Riverside, CA
    Posts
    58

    Derivative of a Vector Proof

    f(t) = real-valued function
    u(t) = vector


    I need help to prove the following:
    d/dt [f(t)u(t)] = f'(t)u(t) + f(t)u'(t)

    I know this is probably easy for you guys, but I haven't had a clue what I am doing for 4+ years now, so if this thing delves into some crazy series summation or something I am prob gonna cry.

    I saw the proof for the dot product of two vectors, but I cannot do it here as I don't think I know what to do when a function is multiplied by a parametrization, I would assume you just parametrize the vector and then go from there, but I don't know what that would look like in a proof, or maybe treat the function as a scalar... sorry idk what I am talking about.

    Thanks,
    -Warren.


    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member 11rdc11's Avatar
    Joined
    Jul 2007
    From
    New Orleans
    Posts
    894
    Quote Originally Posted by Warrenx View Post
    f(t) = real-valued function
    u(t) = vector


    I need help to prove the following:
    d/dt [f(t)u(t)] = f'(t)u(t) + f(t)u'(t)

    I know this is probably easy for you guys, but I haven't had a clue what I am doing for 4+ years now, so if this thing delves into some crazy series summation or something I am prob gonna cry.

    I saw the proof for the dot product of two vectors, but I cannot do it here as I don't think I know what to do when a function is multiplied by a parametrization, I would assume you just parametrize the vector and then go from there, but I don't know what that would look like in a proof, or maybe treat the function as a scalar... sorry idk what I am talking about.

    Thanks,
    -Warren.

    Just think of it as the product rule you learned in calc 1.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Warrenx View Post
    f(t) = real-valued function
    u(t) = vector


    I need help to prove the following:
    d/dt [f(t)u(t)] = f'(t)u(t) + f(t)u'(t)

    I know this is probably easy for you guys, but I haven't had a clue what I am doing for 4+ years now, so if this thing delves into some crazy series summation or something I am prob gonna cry.

    I saw the proof for the dot product of two vectors, but I cannot do it here as I don't think I know what to do when a function is multiplied by a parametrization, I would assume you just parametrize the vector and then go from there, but I don't know what that would look like in a proof, or maybe treat the function as a scalar... sorry idk what I am talking about.

    Thanks,
    -Warren.


    What is \bold{u}? I assume it's a vector valued function \bold{u}:\mathbb{R}\to\mathbb{R}^n:t\mapsto(u_1(t)  ,\cdots,u_n(t)). If so maybe it's easier to think about it by \bold{u}(t)=\sum_{j=1}^{n}u_j(t)e_j (where e_j=(0,\cdots,\underbrace{1}_{j^{\text{th}}\text{ }place},\cdots,0)) and then it should seem obvious that f(t)\bold{u}(t)=\sum_{j=1}^{n}f(t)u_j(t)e_j. But then how do we define the differentiation of this function? Isn't it coordinate-wise? so that \frac{d}{dt}\left(f(t)\bold{u}(t)\right)=\sum_{j=1  }^{n}\frac{d}{dt}(f(t)u_j(t))e_j=\cdots

    Can you finish?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Lie Derivative of a Vector Field
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: November 14th 2011, 03:01 PM
  2. vector question derivative ...
    Posted in the Calculus Forum
    Replies: 0
    Last Post: October 9th 2010, 01:55 PM
  3. Replies: 3
    Last Post: September 18th 2010, 02:31 PM
  4. Replies: 6
    Last Post: July 7th 2010, 11:11 AM
  5. Derivative of an unit vector
    Posted in the Calculus Forum
    Replies: 4
    Last Post: March 29th 2009, 06:09 PM

Search Tags


/mathhelpforum @mathhelpforum