Consider the implicit function of three arguments, \(f ( x , y , z ) = 0\) . Show that \(\frac { \partial z } { \partial y } \cdot \frac { \partial y } { \partial x } \cdot \frac { \partial x } { \partial z } = - 1\) . Give an analogue of this statement for the implicit function of n arguments, \(f ( x _ { 1 } , . . . , x _ { n } ) = 0\)
Triple product rule for partial derivatives of an implicit function
P-TRIV-RA10
- Area
- Real Analysis
- Status
- draft