Consider the function
$ F(x_{1}.......,x_{n}) = \sum_{i=1}^{n} \alpha_{i} ln x_{i}$
where $ \alpha _{i} $ are positive constants, and $x_{i} \geq 1$
Does this function satisfy Euler's theorem?
Euler's theorem is
$ \sum_{i=1}^{n} x_{i} \frac{\partial f(x)}{\partial x_{i}} = m f(x)$
I don't think it does, as
$ x_{1}\frac{\partial \alpha_{1} }{\partial x_{1}} ......... + x_{n}\frac{\partial \alpha_{n} }{\partial x_{n}} $ = $ ( \alpha_{1} ..... + \alpha_{n} ) $ so it does not satisfy eulers theroem as we dont get m f(x) , is this correct ?
also, have I differentiated correctly? Am not too sure,