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

question 254

Multiple Choice

$\text { Find } \mathrm { f } _ { \mathbf { x } } , \mathrm { f } _ { \mathbf { y } } \text {, and } \mathrm { f } _ { \mathbf { Z } }$
- $f ( x , y , z ) = \cos x \sin ^ { 2 } ( y z )$

• A) \(f _ { X } = \sin x \sin ^ { 2 } ( y z ) ; f _ { y } = - 2 z \cos x \sin ( y z ) \cos ( y z ) ; f _ { Z } = - 2 y \cos x \sin ( y z ) \cos ( y z )\)
• B) \(f _ { x } = - \sin x \sin ^ { 2 } ( y z ) ; f _ { y } = 2 z \cos x \sin ( y z ) \cos ( y z ) ; f _ { z } = 2 y \cos x \sin ( y z ) \cos ( y z )\)
• C) \(f _ { x } = \sin x \sin ^ { 2 } ( y z ) ; f _ { y } = - \cos x \sin ( y z ) \cos ( y z ) ; f _ { z } = - \cos x \sin ( y z ) \cos ( y z )\)
• D) \(f _ { X } = - \sin x \sin ^ { 2 } ( y z ) ; f _ { y } = z \cos x \sin ( y z ) \cos ( y z ) ; f _ { z } = y \cos x \sin ( y z ) \cos ( y z )\)

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Definitions:

Marginal Utility

The additional satisfaction or benefit (utility) a consumer gains from consuming one more unit of a good or service.

Supply and Demand

The fundamental economic model describing the balance between the quantity of goods available and the desire of buyers for it.

Marginal Utility

The additional satisfaction a consumer gains from consuming one more unit of a good or service.

Opportunity Cost

The cost of foregoing the next best alternative when making a decision or choice.