Use Implicit Differentiation to Find the Specified Derivative at the Given

Multiple Choice

Use implicit differentiation to find the specified derivative at the given point.
-Find $\frac { \partial z } { \partial y }$ at the point $( 8,1 , - 1 )$ for $\ln \left( \frac { y z } { x } \right) - e ^ { x y + z ^ { 2 } } = 0$ .

A) $\frac { 1 - 2 \mathrm { e } ^ { 9 } } { 1 - 8 \mathrm { e } ^ { 9 } }$
B) $\frac { 2 \mathrm { e } ^ { 9 } - 1 } { 1 - 8 \mathrm { e } ^ { 9 } }$
C) $\frac { 8 \mathrm { e } ^ { 9 } - 1 } { 1 - 2 \mathrm { e } ^ { 9 } }$
D) $\frac { 1 - 8 \mathrm { e } ^ { 9 } } { 1 - 2 \mathrm { e } ^ { 9 } }$