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

question 197

Multiple Choice

Write a chain rule formula for the following derivative.
- $\frac { \partial \mathrm { u } } { \partial \mathrm { x } }$ for $\mathrm { u } = \mathrm { f } ( \mathrm { r } , \mathrm { s } , \mathrm { t } ) ; \mathrm { r } = \mathrm { g } ( \mathrm { y } ) , \mathrm { s } = \mathrm { h } ( \mathrm { z } ) , \mathrm { t } = \mathrm { k } ( \mathrm { x } , \mathrm { z } )$

• A) \(\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = 0\)
• B) \(\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = \frac { \partial \mathrm { u } } { \partial \mathrm { t } }\)
• C) \(\frac { \partial u } { \partial x } = \frac { \partial t } { \partial x }\)
• D) \(\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = \frac { \partial \mathrm { u } } { \partial \mathrm { t } } \frac { \partial \mathrm { t } } { \partial \mathrm { x } }\)

---

Definitions:

Coronary Heart Disease

A condition characterized by the narrowing of the coronary arteries, leading to decreased blood flow to the heart muscle.

Blood Vessels

Tubular structures carrying blood through the tissues and organs; a vital component of the circulatory system.

Clogging

A type of folk dance originating in the Appalachian region where dancers create percussive sounds with their shoes.

Lymphocytes

A type of white blood cell that plays an essential role in the body's immune response.