Use the Chain Rule to Find $\frac { \partial w } { \partial r }$

Use the Chain Rule to find $\frac { \partial w } { \partial r }$ and $\frac { \partial w } { \partial t }$ if $r = 5$ $s = 2$ and $t = 0$ $w = \frac { x ^ { 2 } y } { z ^ { 2 } } , \quad x = r e ^ { s t } , \quad y = s e ^ { n t } , \quad z = e ^ { r s t }$

A) $\frac { \partial w } { \partial r } = 20 , \quad \frac { \partial w } { \partial t } = - 550$
B) $\frac { \partial w } { \partial r } = 100 , \quad \frac { \partial w } { \partial t } = 200$
C) $\frac { \partial w } { \partial r } = 10 , \quad \frac { \partial w } { \partial t } = 0$
D) $\frac { \partial w } { \partial r } = 7 , \quad \frac { \partial w } { \partial t } = - 550$

Correct Answer:

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