2 For \(x , y \in \mathbb { R }\), the function f is given by \(\mathrm { f } ( x , y ) = 2 x ^ { 2 } \mathrm { y } ^ { 7 } + 3 x ^ { 5 } y ^ { 4 } - 5 x ^ { 8 } y\).
- Prove that \(\mathrm { xf } _ { \mathrm { x } } + \mathrm { yf } _ { \mathrm { y } } = \mathrm { nf }\), where \(n\) is a positive integer to be determined.
- Show that \(\mathrm { xf } _ { \mathrm { xx } } + \mathrm { yf } _ { \mathrm { xy } } = ( \mathrm { n } - 1 ) \mathrm { f } _ { \mathrm { x } }\).