$x \dfrac{\partial u}{\partial x} + y \dfrac{\partial u}{\partial y} + z \dfrac{\partial u}{\partial z} $ where $ u \;=\; \dfrac{x^3y^3z^3}{x^3+y^3+z^3} $

Statement: If u=f(x, y, z)is a homogeneous function of degree n, then -

$ \\ x \dfrac{\partial u}{\partial x} + y \dfrac{\partial u}{\partial y} + z \dfrac{\partial u}{\partial z} \;=\; n \cdot u \\ \; \\ \; \\ $

Let, u=f(x, y, z) is a homogeneous function of degree n. …