Find the Requested Partial Derivative $\frac { \partial z } { \partial y }$

question 53

Multiple Choice

Find the requested partial derivative.
- $\frac { \partial z } { \partial y }$ if $z ^ { 3 } = z + x y - 1$ and $y ^ { 3 } = x + y - 1$

• A) \(\frac { x + 3 y ^ { 3 } - y } { 3 z ^ { 2 } + 1 }\)
• B) \(\frac { x - 3 y ^ { 3 } - y } { 3 z ^ { 2 } + 1 }\)
• C) \(\frac { x + 3 y ^ { 3 } - y } { 3 z ^ { 2 } - 1 }\)
• D) \(\frac { x - 3 y ^ { 3 } - y } { 3 z ^ { 2 } - 1 }\)

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Definitions:

Equilibrium Price

The market price at which the quantity of goods demanded equals the quantity supplied, leading to market stability.

Market Demand

The combined volume of a good or service that consumers in a marketplace are ready and capable of buying at assorted prices.

Marginal Cost

The funding necessary to manufacture an extra unit of a good or service.

Average Variable Cost

The total variable costs (costs that change with production volume) divided by the quantity of output produced.