Partial derivative

1. Mar 18, 2009

ak123456

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

2. Relevant equations

3. The attempt at a solution
set g($$\lambda$$)=f($$\lambda$$x)
find out g'(1)
then how to continue ?

2. Mar 19, 2009

ak123456

any help?

3. Mar 19, 2009

Office_Shredder

Staff Emeritus
$$g( \lambda _ = f( \lambda x)$$

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

The right hand side is obtained using the chain rule. Try to calculate what the right hand side really is

4. Mar 19, 2009

ak123456

i don't know where is the formula for g' comes from

5. Mar 20, 2009

HallsofIvy

Staff Emeritus
Office Shredder told you: it is the chain rule.