Partial derivative

  • Thread starter ak123456
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  • #1
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Homework Statement


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)



Homework Equations





The Attempt at a Solution


set g([tex]\lambda[/tex])=f([tex]\lambda[/tex]x)
find out g'(1)
then how to continue ?
 

Answers and Replies

  • #2
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any help?
 
  • #3
Office_Shredder
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[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
 
  • #4
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[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

i don't know where is the formula for g' comes from
 
  • #5
HallsofIvy
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Office Shredder told you: it is the chain rule.
 

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