Find the Gradient Field of the Function $$f ( x , y , z ) = \ln \left( \frac { ( x + y ) ^ { 3 } } { z ^ { 10 } } \right) + z ^ { 9 }$$

question 230

Multiple Choice

Find the gradient field of the function.
- $$f ( x , y , z ) = \ln \left( \frac { ( x + y ) ^ { 3 } } { z ^ { 10 } } \right) + z ^ { 9 }$$

• A)\({\nabla} f = \frac { 3 } { \mathrm { x } } \mathrm { i } + \frac { 3 } { \mathrm { y } } \mathrm { j } + \left( 9 \mathrm { z } ^ { 8 } + \frac { 10 } { \mathrm { z } } \right) \mathbf { k }\)
• B) \({\nabla} f = \frac { 3 } { \mathrm { x } + \mathrm { y } } \mathrm { i } + \frac { 3 } { \mathrm { x } + \mathrm { y } } \mathrm { j } + \left( 9 \mathrm { z } ^ { 8 } + \frac { 10 } { \mathrm { z } } \right) \mathrm { k }\)
• C)\({\nabla} f = \frac { 3 } { x + y } i + \frac { 3 } { x + y } j + \left( 9 z ^ { 8 } - \frac { 10 } { z } \right) k\)
• D) \({\nabla} f = \frac { 3 } { \mathrm { x } } \mathrm { i } + \frac { 3 } { \mathrm { y } } \mathrm { j } + \left( 9 \mathrm { z } ^ { 8 } - \frac { 10 } { \mathrm { z } } \right) \mathbf { k }\)

Distinguish the difference between number of occurrences and rates in graphical representations.

Understand how manipulating the axes can affect the appearance of trends in graphs.

Critically analyze the effectiveness and clarity of graphical representations in conveying data.

Identify fair practices in representing and comparing statistical data.

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