$x = 8 t \sin s , y = 8 t \cos s$

Multiple Choice

$\text { Find } \frac { \partial w } { \partial t } \text { using the appropriate Chain Rule for } w = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \text { where }$ $x = 8 t \sin s , y = 8 t \cos s$ , and $z = 5 s t ^ { 2 }$ .

A) $128 t + 100 s ^ { 2 } t ^ { 3 }$
B) $50 t + 256 s ^ { 2 } t ^ { 3 }$
C) $128 t ^ { 2 } + 50 s ^ { 3 } t ^ { 2 }$
D) $128 t + 256 s ^ { 3 } t ^ { 2 }$
E) $128 t ^ { 2 } + 50 s ^ { 2 } t ^ { 3 }$