Write a Chain Rule Formula for the Following Derivative A)

question 302

Multiple Choice

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

• A) \(\frac { \partial \mathrm { w } } { \partial \mathrm { t } } = \frac { \mathrm { dp } } { \mathrm { dt } } + \frac { \mathrm { dq } } { \mathrm { dt } } + \frac { \mathrm { dr } } { \mathrm { dt } }\)
• B) \(\frac { \partial \mathrm { w } } { \partial \mathrm { t } } = \frac { \partial \mathrm { w } } { \partial \mathrm { p } } \frac { \mathrm { dt } } { \mathrm { dp } } + \frac { \partial \mathrm { w } } { \partial \mathrm { q } } \frac { \mathrm { dt } } { \mathrm { dq } } + \frac { \partial \mathrm { w } } { \partial \mathrm { r } } \frac { \mathrm { dt } } { \mathrm { dr } }\)
• C) \(\frac { \partial \mathrm { w } } { \partial \mathrm { t } } = \frac { \partial \mathrm { w } } { \partial \mathrm { p } } + \frac { \partial \mathrm { w } } { \partial \mathrm { q } } + \frac { \partial \mathrm { w } } { \partial \mathrm { r } }\)
• D) \(\frac { \partial \mathrm { w } } { \partial \mathrm { t } } = \frac { \partial \mathrm { w } } { \partial \mathrm { p } } \frac { \mathrm { dp } } { \mathrm { dt } } + \frac { \partial \mathrm { w } } { \partial \mathrm { q } } \frac { \mathrm { dq } } { \mathrm { dt } } + \frac { \partial \mathrm { w } } { \partial \mathrm { r } } \frac { \mathrm { dr } } { \mathrm { dt } }\)

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