Write a Chain Rule Formula for the Following Derivative $\frac { \partial w } { \partial x }$

question 189

Multiple Choice

Write a chain rule formula for the following derivative.
- $\frac { \partial w } { \partial x }$ for $w = f ( p , q ) ; p = g ( x , y ) , q = h ( x , y )$

• A) \(\frac { \partial w } { \partial x } = \frac { \partial w } { \partial p } \frac { \partial p } { \partial x } + \frac { \partial w } { \partial q } \frac { \partial q } { \partial x }\)
• B) \(\frac { \partial w } { \partial x } = \frac { \partial w } { \partial p } \frac { \partial p } { \partial x }\)
• C) \(\frac { \partial w } { \partial x } = \frac { \partial w } { \partial x } \frac { \partial x } { \partial p } + \frac { \partial w } { \partial x } \frac { \partial x } { \partial q }\)
• D) \(\frac { \partial w } { \partial x } = \frac { \partial w } { \partial p } + \frac { \partial w } { \partial q }\)

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Definitions:

Opponent-Process Theory

A psychological and neurological model that explains how the perception of colors results from opposing neural processes.

Chromatic/Achromatic

Refers to colors with hue (chromatic) and without hue (achromatic), such as black, white, and grays.

Opponent-Process Pairs

A theory suggesting that the human visual system interprets colors in an antagonistic way, through pairs of colors opposite each other on the color spectrum.

Young-Helmholtz Theory

A theory of color vision proposing that the human eye perceives color because it has three types of receptors, each sensitive to red, green, or blue light.