Provide an appropriate answer.
-Find $\frac { \partial \mathrm { w } } { \partial \mathrm { r } }$ when $\mathrm { r } = 5$ and $\mathrm { s } = - 2$ if $\mathrm { w } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \mathrm { xz } + \mathrm { y } ^ { \wedge } 2 , \mathrm { x } = 3 \mathrm { r } + 7 , \mathrm { y } = \mathrm { r } + \mathrm { s }$, and $\mathrm { z } = \mathrm { r } - \mathrm { s }$
A) $\frac { \partial w } { \partial r } = 49$
B) $\frac { \partial w } { \partial r } = 25$
C) $\frac { \partial w } { \partial r } = 21$
D) $\frac { \partial w } { \partial r } = 39$

Question

Quizplus · Accepted Answer

$\frac { \partial w } { \partial r } = 49$ because $$\frac { \partial w } { \partial r } = \frac { \partial w } { \partial x } \frac { \partial x } { \partial r } + \frac { \partial w } { \partial y } \frac { \partial y } { \partial r } + \frac { \partial w } { \partial z } \frac { \partial z } { \partial r }$$$$= ( z + 2 y y ) ( 3 ) + ( 2 y ) ( 1 ) + ( x - ( - s ) ) ( 1 )$$$$= ( 5 - 2 ( - 2 ) ( 5 ) + 2 ( - 2 ) ( - 2 ) ) ( 3 ) + ( 2 ( - 2 ) ) ( 1 ) + ( 3 ( 5 ) + 7 - ( - 2 ) ) ( 1 )$$$$= ( 5 + 20 + 8 ) ( 3 ) - 4 + 22$$$$= 33 ( 3 ) - 4 + 22 = 49$$

Provide an Appropriate Answer ∂w∂r\frac { \partial \mathrm { w } } { \partial \mathrm { r } }∂r∂w​

Provide an Appropriate Answer $\frac { \partial \mathrm { w } } { \partial \mathrm { r } }$