# Partial derivative

## Homework Statement

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)

## The Attempt at a Solution

set g($$\lambda$$)=f($$\lambda$$x)
find out g'(1)
then how to continue ?

any help?

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

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

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

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

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

HallsofIvy