Find the Total Differential for the Function $w = e ^ { y } \cos ( x ) + z ^ { 4 }$

question 15

Multiple Choice

Find the total differential for the function $w = e ^ { y } \cos ( x ) + z ^ { 4 }$

• A) \( d w = - 2 e ^ { y } \sin ( x ) d x + e ^ { y } \cos ( x ) d y + 4 z ^ { 5 } d z\)
• B) \(d w = e ^ { y } \cos ( x ) d x + e ^ { y } \cos ( x ) d y + 4 z ^ { 3 } d z\)
• C) \(d w = e ^ { y } \sin ( x ) d x - e ^ { y } \cos ( x ) d y - 4 z ^ { 3 } d z\)
• D) \(d w = - e ^ { y } \cos ( x ) d x + e ^ { y } \cos ( x ) d y + 4 z ^ { 5 } d z\)
• E) \(d w = - e ^ { y } \sin ( x ) d x + e ^ { y } \cos ( x ) d y + 4 z ^ { 3 } d z\)

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Definitions:

Personality Traits

Enduring characteristics or behaviors that define an individual's patterns of feeling, thinking, and acting across different situations.

Genetically Determined

Traits or characteristics that are influenced by genes inherited from parents.

Reinforcement

In behavioral psychology, it is the process of encouraging or establishing a pattern of behavior by offering reward or punishment.

Psychoanalytic

Pertaining to psychoanalysis, the theory and therapy developed by Freud that focuses on exploring unconscious desires and conflicts.