$\text { Find } \mathrm { f } _ { \mathbf { x } } , \mathrm { f } _ { \mathbf { y } } \text {, and } \mathrm { f } _ { \mathbf { Z } }$

question 366

Multiple Choice

$\text { Find } \mathrm { f } _ { \mathbf { x } } , \mathrm { f } _ { \mathbf { y } } \text {, and } \mathrm { f } _ { \mathbf { Z } }$
- $$f ( x , y , z ) = \ln ( x y ) ^ { z }$$

• A) \(\mathrm { f } _ { \mathrm { X } } = \mathrm { z } \ln \frac { \mathrm { z } } { \mathrm { x } } ; \mathrm { f } _ { \mathrm { y } } = \mathrm { z } \ln \frac { \mathrm { z } } { \mathrm { y } } ; \mathrm { f } _ { \mathrm { Z } } = \ln ( \mathrm { xy } )\)
• B) \(f _ { X } = - \frac { z } { x } ; f _ { y } = - \frac { z } { y } ; f _ { z } = \ln ( x y )\)
• C) \(\mathrm { f } _ { \mathrm { X } } = \frac { \mathrm { z } } { \mathrm { x } } ; \mathrm { f } _ { \mathrm { y } } = \frac { \mathrm { z } } { \mathrm { y } } ; \mathrm { f } _ { \mathrm { Z } } = \mathrm { z } \ln ( \mathrm { xy } ) ^ { \mathrm { z } - 1 }\)
• D) \(\mathrm { f } _ { \mathrm { X } } = \frac { \mathrm { z } } { \mathrm { x } } ; \mathrm { f } _ { \mathrm { y } } = \frac { \mathrm { z } } { \mathrm { y } } ; \mathrm { f } _ { \mathrm { Z } } = \ln ( \mathrm { xy } )\)

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