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!

Homework Help: Partial derivative

  1. Mar 18, 2009 #1
    1. The problem statement, all variables and given/known data
    A function f: R^n--R is homogenous of degree p if f( [tex]\lambda[/tex]x)=[tex]\lambda[/tex]^p f(x) for all [tex]\lambda[/tex][tex]\in[/tex]R and all x[tex]\in[/tex]R^n
    show that if f is differentiable at x ,then x[tex]\nabla[/tex]f(x)=pf(x)

    2. Relevant equations

    3. The attempt at a solution
    set g([tex]\lambda[/tex])=f([tex]\lambda[/tex]x)
    find out g'(1)
    then how to continue ?
  2. jcsd
  3. Mar 19, 2009 #2
    any help?
  4. Mar 19, 2009 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    [tex] g( \lambda _ = f( \lambda x)[/tex]

    Then [tex]g'( \lambda ) = \sum_{i=1}^{n} \frac{df}{dx_i} \frac{d( \lambda x}{dx_i}[/tex]

    The right hand side is obtained using the chain rule. Try to calculate what the right hand side really is
  5. Mar 19, 2009 #4
    i don't know where is the formula for g' comes from
  6. Mar 20, 2009 #5


    User Avatar
    Science Advisor

    Office Shredder told you: it is the chain rule.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook