Write a Chain Rule Formula for the Following Derivative A)

question 196

Multiple Choice

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

• A) \(\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = \frac { \partial \mathrm { u } } { \partial \mathrm { p } } \frac { \partial \mathrm { p } } { \partial \mathrm { x } } + \frac { \partial \mathrm { u } } { \partial \mathrm { q } } \frac { \partial \mathrm { q } } { \partial \mathrm { x } }\)
• B) \(\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = \frac { \partial \mathrm { u } } { \partial \mathrm { p } } \frac { \partial \mathrm { x } } { \partial \mathrm { p } } + \frac { \partial \mathrm { u } } { \partial \mathrm { q } } \frac { \partial \mathrm { x } } { \partial \mathrm { q } }\)
• C) \(\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = \frac { \partial \mathrm { u } } { \partial \mathrm { q } } \frac { \partial \mathrm { q } } { \partial \mathrm { x } }\)
• D) \(\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = \frac { \partial \mathrm { u } } { \partial \mathrm { p } } \frac { \partial \mathrm { p } } { \partial \mathrm { x } } + \frac { \partial \mathrm { u } } { \partial \mathrm { q } } \frac { \partial \mathrm { q } } { \partial \mathrm { y } } + \frac { \partial \mathrm { u } } { \partial \mathrm { q } } \frac { \partial \mathrm { q } } { \partial \mathrm { z } }\)

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