If $z = x ^ { 2 } \sin y + y e ^ { x }$

question 16

Essay

If $z = x ^ { 2 } \sin y + y e ^ { x }$ , find $\frac { \delta z } { \delta x } , \frac { \delta z } { \delta y } , \frac { \delta ^ { 2 } z } { \delta x ^ { 2 } } , \frac { \delta ^ { 2 } z } { \delta x \delta y } \text {, and } \frac { \delta ^ { 2 } z } { \delta y ^ { 2 } }$

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Definitions:

Coase Theorem

A legal and economic theory that states that if trade in an externality is possible and there are no transaction costs, bargaining will lead to an efficient outcome regardless of the initial allocation of property.

Taxes

Compulsory financial charges or levies collected by governments from businesses and individuals to fund public expenditures.

Negative Externalities

Costs suffered by a third party due to an economic transaction that they were not a part of.

Coase Theorem

A principle that asserts that if property rights are well-defined and transaction costs are negligible, parties will negotiate to correct externalities and allocate resources efficiently.