$F(x,y)$ is homogenous of degree n if $f(tx,ty)=t^nf(x,y)$. Verify that
- $xf_x(x,y)+yf_y(x,y)=nf(x,y)$
- $x^2f_{xx}(x,y)+2xyf_{xy}+y^2f_{yy}(x,y)=n(n-1)f(x,y)$
Looks like I need enlightenment again... Hopefully, its not another embarrassingly simple thing I missed out in another question
What I tried:
$f_x(x,y)=t^nf_x(x,y)$
$f_y(x,y)=t^nf_y(x,y)$
$xt^nf_x(x,y) + yt^nf_y(x,y) = t^n(xf_x(x,y) + yf_y(x,y))$
Doesn't look like I am doing the right thing?