$\text { Find } \frac { \partial w } { \partial s } \text { using the appropriate Chain Rule for } w = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \text { where }$ $x = 8 t \sin s , y = 8 t \cos s$, and $z = 8 s t ^ { 2 }$
A) $64 s t ^ { 4 }$
B) $128 s ^ { 4 } t$
C) $16 s ^ { 4 } t$
D) $1285 t ^ { 4 }$
E) $16 s t ^ { 4 }$

Question

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The Answer of $\text { Find } \frac { \partial w } { \partial s } \text { using the appropriate Chain Rule for } w = x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \text { where }$ $x = 8 t \sin s , y = 8 t \cos s$, and $z = 8 s t ^ { 2 }$
A) $64 s t ^ { 4 }$
B) $128 s ^ { 4 } t$
C) $16 s ^ { 4 } t$
D) $1285 t ^ { 4 }$
E) $16 s t ^ { 4 }$

x=8tsin⁡s,y=8tcos⁡sx = 8 t \sin s , y = 8 t \cos sx=8tsins,y=8tcoss

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