Use Implicit Differentiation to Find the Specified Derivative at the Given

question 374

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) \(\frac { 1 - 8 \mathrm { e } ^ { 9 } } { 1 - 2 \mathrm { e } ^ { 9 } }\)

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