Find the Total Differential of the Function $$z = 2 x ^ { 8 } y ^ { 3 }$$

question 2

Multiple Choice

Find the total differential of the function $$z = 2 x ^ { 8 } y ^ { 3 }$$

• A) \(d z = 16 x ^ { 8 } y ^ { 3 } d x + 6 x ^ { 8 } y ^ { 3 } d y\)
• B) \(d z = 48 x ^ { 7 } y ^ { 3 } d x + 48 x ^ { 8 } y ^ { 2 } d y\)
• C) \(d z = 2 x ^ { 2 } y ^ { 8 } d x + 2 x ^ { 3 } y ^ { 7 } d y\)
• D) \(d z = 16 x ^ { 7 } y ^ { 3 } d x + 6 x ^ { 8 } y ^ { 2 } d y\)
• E) \(d z = 6 x ^ { 2 } y ^ { 8 } d x + 16 x ^ { 3 } y ^ { 7 } d y\)

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Definitions:

Implicit Coercion

A form of pressure or influence that is not explicitly stated but is understood or implied in interactions.

Risky

Involving or exposed to a high degree of uncertainty and the potential for loss or harm.

Tempered Radicals

Individuals within organizations who drive change by challenging norms and promoting progressive policies, while managing to stay within the corporate system.

Manipulation

Influencing or controlling someone or something to one's advantage, often in a deceitful or unfair way.