Find the First Partial Derivatives with Respect to X, Y $w = \frac { 9 x z } { 8 x + 4 y }$

question 54

Multiple Choice

Find the first partial derivatives with respect to x, y, and z. $w = \frac { 9 x z } { 8 x + 4 y }$

• A) \(\frac { \partial w } { \partial x } = \frac { 36 x z } { ( 8 x + 4 y ) ^ { 2 } } , \frac { \partial w } { \partial y } = - \frac { 36 y z } { ( 8 x + 4 y ) ^ { 2 } } , \frac { \partial w } { \partial z } = \frac { 9 x } { 8 x + 4 y }\)
• B) \(\frac { \partial w } { \partial x } = \frac { 36 x z } { 8 x + 4 y } , \frac { \partial w } { \partial y } = - \frac { 36 y z } { 8 x + 4 y } , \frac { \partial w } { \partial z } = \frac { 9 x } { ( 8 x + 4 y ) ^ { 2 } }\)
• C) \(\frac { \partial w } { \partial x } = \frac { 36 y z } { 8 x + 4 y } , \frac { \partial w } { \partial y } = - \frac { 36 x z } { 8 x + 4 y } , \frac { \partial w } { \partial z } = \frac { 9 x } { ( 8 x + 4 y ) ^ { 2 } }\)
• D) \(\frac { \partial w } { \partial x } = \frac { 36 y z } { ( 8 x + 4 y ) ^ { 2 } } , \frac { \partial w } { \partial y } = - \frac { 36 x z } { ( 8 x + 4 y ) ^ { 2 } } , \frac { \partial w } { \partial z } = \frac { 9 x } { 8 x + 4 y }\)
• E) \(\frac { \partial w } { \partial x } = \frac { 36 y z } { ( 8 x + 4 y ) ^ { 2 } } , \frac { \partial w } { \partial y } = - \frac { 36 x z } { ( 8 x + 4 y ) ^ { 2 } } , \frac { \partial w } { \partial z } = \frac { 9 x } { ( 8 x + 4 y ) ^ { 2 } }\)

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