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Math Help - homogeneous function of degree n

  1. #1
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    homogeneous function of degree n

    I need to prove that if f is differentiable on R and homogeneous of degree n, then xf'(x)=nf(x).
    [Homogeneous of degree n means f(tx)=f(x)t^n for every t>0 such that x and tx are in R.]
    Ive tried various rearrangements of the equations but nothing has looked too promising. What should I do?
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  2. #2
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    Take g(t)=f(tx)=f(x)t^n then g is obviously differentiable whenever f is, and by the chain rule: g'(t)=f'(tx)x=nf(x)t^{n-1}, and taking t=1 the result follows.
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