Find the Gradient Field of the Function $f ( x , y , z ) = e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } }$

question 129

Multiple Choice

Find the gradient field of the function.
- $f ( x , y , z ) = e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } }$

• A) \(\nabla f = x ^ { 6 } e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } } i + y ^ { 5 } e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } } j + z ^ { 7 } e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } } \mathbf { k }\)
• B) \({\nabla} f = 6 \mathrm { x } ^ { 5 } \mathrm { e } ^ { \mathrm { x } ^ { 6 } } \mathbf { i } + 5 \mathrm { y } ^ { 4 } \mathrm { e } ^ { 5 } \mathbf { j } + 7 \mathrm { z } ^ { 6 } \mathrm { e } ^ { \mathrm { z } ^ { 7 } } \mathbf { k }\)
• C) \({\nabla} f = 6 x ^ { 5 } e ^ { x ^ { 6 } } + y ^ { 5 } + z ^ { 7 } i + 5 y ^ { 4 } e ^ { x ^ { 6 } } + y ^ { 5 } + z ^ { 7 } j + 7 z ^ { 6 } e ^ { x ^ { 6 } } + y ^ { 5 } + z ^ { 7 } k\)
• D) \(\nabla f = x ^ { 5 } e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } } i + y ^ { 4 } e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } } j + z ^ { 6 } e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } } \mathbf { k }\)

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