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

Question 197

Multiple Choice

Write a chain rule formula for the following derivative.
- ux\frac { \partial \mathrm { u } } { \partial \mathrm { x } } for u=f(r,s,t) ;r=g(y) ,s=h(z) ,t=k(x,z) \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) ux=0\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = 0
B) ux=ut\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = \frac { \partial \mathrm { u } } { \partial \mathrm { t } }
C) ux=tx\frac { \partial u } { \partial x } = \frac { \partial t } { \partial x }
D) ux=uttx\frac { \partial \mathrm { u } } { \partial \mathrm { x } } = \frac { \partial \mathrm { u } } { \partial \mathrm { t } } \frac { \partial \mathrm { t } } { \partial \mathrm { x } }

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