Write a Chain Rule Formula for the Following Derivative A)

question 219

Multiple Choice

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

• A) \(\frac { \partial \mathrm { w } } { \partial \mathrm { t } } = \frac { \partial \mathrm { w } } { \partial \mathrm { x } } \frac { \partial \mathrm { x } } { \partial \mathrm { t } } + \frac { \partial \mathrm { w } } { \partial \mathrm { y } } \frac { \partial \mathrm { y } } { \partial \mathrm { t } }\)
• B) \(\frac { \partial \mathrm { w } } { \partial \mathrm { t } } = \frac { \partial \mathrm { w } } { \partial \mathrm { x } } \frac { \partial \mathrm { x } } { \partial \mathrm { r } } + \frac { \partial \mathrm { w } } { \partial \mathrm { y } } \frac { \partial \mathrm { y } } { \partial \mathrm { s } } + \frac { \partial \mathrm { w } } { \partial \mathrm { z } } \frac { \partial \mathrm { z } } { \partial \mathrm { t } }\)
• C) \(\frac { \partial w } { \partial t } = \frac { \partial w } { \partial x } + \frac { \partial w } { \partial y } + \frac { \partial w } { \partial z }\)
• D) \(\frac { \partial \mathrm { w } } { \partial \mathrm { t } } = \frac { \partial \mathrm { w } } { \partial \mathrm { x } } \frac { \partial \mathrm { x } } { \partial \mathrm { t } } + \frac { \partial \mathrm { w } } { \partial \mathrm { y } } \frac { \partial \mathrm { y } } { \partial \mathrm { t } } + \frac { \partial \mathrm { w } } { \partial \mathrm { z } } \frac { \partial \mathrm { z } } { \partial \mathrm { t } }\)

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