Results 1 to 8 of 8

Math Help - differentiable functions

  1. #1
    Super Member
    Joined
    Aug 2009
    Posts
    639

    differentiable functions




    can some kind soul tell me what is this question asking and how to solve it?
    Last edited by alexandrabel90; January 10th 2010 at 08:39 AM. Reason: couldnt see the image
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member
    Joined
    Mar 2008
    From
    Pennsylvania, USA
    Posts
    269
    Thanks
    37
    The product rule for two functions is given by

     (f \cdot g)' = f' \cdot g  + f \cdot g\

    Using induction, prove that for any  n\geq2 number of functions, the generalized product rule (given to you) holds.

    Start with your base case. Assume. Work up.
    Last edited by abender; January 10th 2010 at 09:00 AM. Reason: latex poop
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Aug 2009
    Posts
    639
    may i know what does the LHS N look a like symbol from k=1 to n mean? this is the first time im seeing that symbol thats why.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Senior Member
    Joined
    Mar 2008
    From
    Pennsylvania, USA
    Posts
    269
    Thanks
    37
     \mathbf{Z}^{+} represents the set of positive integers. 1, 2, 3, ...


     \mathbf{R} represents the set of real numbers.
    1, 905, -763, 0.13244, 0, 2/5, anything that is real (read: not imaginary; no i)

     \sum represents "the sum of." So,  \sum_{k=1}^n x^k = x^1 + x^2 + x^3 + ... + x^n


     \prod represents "the product of." So,  \prod_{k=1}^n x^k = x^1 \cdot x^2 \cdot x^3 \cdot ... \cdot x^n
    Last edited by abender; January 10th 2010 at 11:05 AM. Reason: R....not R+
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Super Member
    Joined
    Aug 2009
    Posts
    639



    this is how i have done it..but i got stuck as to how to continue from there..
    Follow Math Help Forum on Facebook and Google+

  6. #6
    No one in Particular VonNemo19's Avatar
    Joined
    Apr 2009
    From
    Detroit, MI
    Posts
    1,823
    Quote Originally Posted by abender View Post
     \mathbf{Z}^{+} represents the set of positive integers. 1, 2, 3, ...


    ?  \mathbf{R}^{+} ? represents the set of real numbers.
    1, 905, -763, 0.13244, 0, 2/5, anything that is real (read: not imaginary; no i)

     \sum represents "the sum of." So,  \sum_{k=1}^n x^k = x^1 + x^2 + x^3 + ... + x^n


     \prod represents "the product of." So,  \prod_{k=1}^n x^k = x^1 \cdot x^2 \cdot x^3 \cdot ... \cdot x^n
    .
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Super Member
    Joined
    Aug 2009
    Posts
    639
    how do you show that A(n+1) = 0 from my working and hence the equation is true by induction?
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Senior Member
    Joined
    Mar 2008
    From
    Pennsylvania, USA
    Posts
    269
    Thanks
    37
    Quote Originally Posted by VonNemo19 View Post
    .
    oops, i was copy-pasting from the latex code above obviously...
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Differentiable Functions
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: January 9th 2011, 08:13 PM
  2. Replies: 9
    Last Post: December 17th 2010, 09:13 AM
  3. [SOLVED] Differentiable FUnctions
    Posted in the Calculus Forum
    Replies: 4
    Last Post: September 30th 2010, 05:20 AM
  4. Set of twice differentiable functions
    Posted in the Calculus Forum
    Replies: 1
    Last Post: May 23rd 2009, 09:36 AM
  5. Sequence of differentiable functions, non-differentiable limit
    Posted in the Differential Geometry Forum
    Replies: 3
    Last Post: April 3rd 2009, 06:13 AM

Search Tags


/mathhelpforum @mathhelpforum