Given $f ( x , y ) = x ^ { 2 } \sin ( x y )$

question 55

Essay

Given $f ( x , y ) = x ^ { 2 } \sin ( x y )$ , find $f _ { x }$ , $f _ { y }$ , and $f _ { x y }$ .

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Definitions:

Autonomic Nervous System

Part of the nervous system that controls involuntary bodily functions, such as heart rate, digestion, and respiratory rate.

Sympathetic

Relating to the part of the autonomic nervous system that typically increases alertness, heart rate, and blood pressure in response to stress.

Parasympathetic

referring to the part of the autonomic nervous system responsible for conserving energy and slowing down the heart rate, among other functions.

Autonomic Nervous System

A component of the nervous system that regulates involuntary physiological processes including heart rate, blood pressure, respiration, digestion, and sexual arousal.