Write a Chain Rule Formula for the Following Derivative A) $\frac { \partial z } { \partial t } = \frac { \partial z } { \partial r } \frac { d r } { d s }$

question 27

Multiple Choice

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

• A) \(\frac { \partial z } { \partial t } = \frac { \partial z } { \partial r } \frac { d r } { d s }\)
• B) \(\frac { \partial \mathrm { z } } { \partial \mathrm { t } } = \frac { \partial \mathrm { z } } { \partial \mathrm { r } } \frac { \mathrm { dr } } { \mathrm { dt } } + \frac { \partial \mathrm { z } } { \partial \mathrm { s } } \frac { \mathrm { ds } } { \mathrm { dt } }\)
• C) \(\frac { \partial \mathrm { z } } { \partial \mathrm { t } } = \frac { \mathrm { dr } } { \mathrm { dt } } + \frac { \mathrm { ds } } { \mathrm { dt } }\)
• D) \(\frac { \partial \mathrm { z } } { \partial \mathrm { t } } = \frac { \partial \mathrm { z } } { \partial \mathrm { r } } \frac { \mathrm { dt } } { \mathrm { dr } } + \frac { \partial \mathrm { z } } { \partial \mathrm { s } } \frac { \mathrm { dt } } { \mathrm { ds } }\)

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