Let $x ^ { 3 } y + y ^ { 3 } z + z ^ { 3 } x = 4$

question 73

Multiple Choice

Let $x ^ { 3 } y + y ^ { 3 } z + z ^ { 3 } x = 4$ , find $\frac { \delta z } { \delta y }$ .

• A) \(\frac { 3 x ^ { 2 } y + z ^ { 3 } } { y ^ { 3 } + 3 z ^ { 2 } x }\)
• B) \(- \frac { 3 y ^ { 2 } z + x ^ { 3 } } { y ^ { 3 } + 3 z ^ { 2 } x }\)
• C) \(\frac { y ^ { 3 } + 3 z ^ { 2 } x } { 3 y ^ { 2 } z + x ^ { 3 } }\)
• D) \(- \frac { y ^ { 3 } + 3 z ^ { 2 } x } { 3 x ^ { 2 } y + z ^ { 3 } }\)
• E) \(- \frac { 3 x ^ { 2 } y + z ^ { 3 } } { y ^ { 3 } + 3 z ^ { 2 } x }\)
• F) \(\frac { 3 y ^ { 2 } z + x ^ { 3 } } { y ^ { 3 } + 3 z ^ { 2 } x }\)
• G) \(- \frac { y ^ { 3 } + 3 z ^ { 2 } x } { 3 y ^ { 2 } z + x ^ { 3 } }\)
• H) \(\frac { y ^ { 3 } + 3 z ^ { 2 } x } { 3 x ^ { 2 } y + z ^ { 3 } }\)

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Definitions:

Time Inconsistent

When preferences change over time in such a way that what is preferred at one point in time is inconsistent with what is preferred at another time.

Central Bankers

Officials responsible for controlling a country's money supply and monetary policy, often through a central bank.

Policymakers

Individuals or groups responsible for making decisions and guidelines that affect the public policies of a nation.

Skepticism

The attitude of doubting the truth of something, such as claims, statements, or the validity of certain beliefs.