Give an Appropriate Answer $$f ( x , y ) = \sin ^ { 2 } \left( - 2 x y ^ { 2 } - y \right)$$

question 15

Multiple Choice

Give an appropriate answer.
- $$f ( x , y ) = \sin ^ { 2 } \left( - 2 x y ^ { 2 } - y \right)$$

• A) \(\frac { \partial f } { \partial x } = 2 \sin \left( - 2 x y ^ { 2 } - y \right) \cos \left( - 2 x y ^ { 2 } - y \right) ; \frac { \partial f } { \partial y } = ( - 8 x - 2 ) \sin \left( - 2 x y ^ { 2 } - y \right) \cos \left( - 2 x y ^ { 2 } - y \right)\)
• B) \(\frac { \partial f } { \partial x } = 2 \sin \left( - 2 x y ^ { 2 } - y \right) \cos \left( - 2 x y ^ { 2 } - y \right) ; \frac { \partial f } { \partial y } = 2 \sin \left( - 2 x y ^ { 2 } - y \right) \cos \left( - 2 x y ^ { 2 } - y \right)\)
• C) \(\frac { \partial f } { \partial x } = - 4 y ^ { 2 } \sin \left( - 2 x y ^ { 2 } - y \right) \cos \left( - 2 x y ^ { 2 } - y \right) ; \frac { \partial f } { \partial y } = ( - 8 x y - 2 ) \sin \left( - 2 x y ^ { 2 } - y \right) \cos \left( - 2 x y ^ { 2 } - y \right)\)
• D) \(\frac { \partial f } { \partial x } = - 4 y ^ { 2 } \sin \left( - 2 x y ^ { 2 } - y \right) \cos \left( - 2 x y ^ { 2 } - y \right) ; \frac { \partial f } { \partial y } = 2 \sin \left( - 2 x y ^ { 2 } - y \right) \cos \left( - 2 x y ^ { 2 } - y \right)\)

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The point at which the quantity of goods consumed by a consumer maximizes their utility, given their budget constraints.

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