Find the Gradient Field of the Function $$f ( x , y , z ) = \left( \frac { x + y } { y + z } \right) ^ { 6 }$$

question 262

Multiple Choice

Find the gradient field of the function.
- $$f ( x , y , z ) = \left( \frac { x + y } { y + z } \right) ^ { 6 }$$

• A) \({\nabla} f = \frac { 6 ( x + y ) ^ { 5 } } { ( y + z ) ^ { 6 } } i + \frac { 6 ( x + y ) ^ { 5 } ( z - x ) } { ( y + z ) ^ { 7 } } j - 6 \frac { ( x + y ) ^ { 6 } } { ( y + z ) ^ { 7 } } \mathbf { k }\)
• B) \({\nabla} f = 6 \left( \frac { x + y } { y + z } \right) ^ { 5 } i + \frac { 6 ( x + y ) ^ { 5 } ( z + x ) } { ( y + z ) ^ { 7 } } j + 6 \frac { ( x + y ) ^ { 6 } } { ( y + z ) ^ { 7 } } k\)
• C)\({\nabla} f = 6 \left( \frac { x + y } { y + z } \right) ^ { 5 } i + \frac { 6 ( x + y ) ^ { 5 } ( z - x ) } { ( y + z ) ^ { 7 } } j + 6 \frac { ( x + y ) ^ { 6 } } { ( y + z ) ^ { 7 } } \mathbf { k }\)
• D)\({\nabla} f = 6 \left( \frac { x + y } { y + z } \right) ^ { 5 } i + \frac { 6 ( x + y ) ^ { 5 } ( z + x ) } { ( y + z ) ^ { 7 } } j - 6 \frac { ( x + y ) ^ { 6 } } { ( y + z ) ^ { 7 } } k\)

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