Find the Gradient Field of the Function $f ( x , y , z ) = \ln \left( x ^ { 4 } + y ^ { 5 } + z ^ { 6 } \right)$

question 71

Multiple Choice

Find the gradient field of the function.
- $f ( x , y , z ) = \ln \left( x ^ { 4 } + y ^ { 5 } + z ^ { 6 } \right)$

• A) \(\nabla \mathrm { f } = \frac { 4 } { x } \ln \left( y ^ { 5 } + z ^ { 6 } \right) i + \frac { 5 } { y } \ln \left( x ^ { 4 } + z ^ { 6 } \right) j + \frac { 6 } { z } \ln \left( x ^ { 4 } + y ^ { 5 } \right) \mathbf { k }\)
• B) \(\nabla f = \frac { 4 x ^ { 3 } } { x ^ { 4 } + y ^ { 5 } + z ^ { 6 } } i + \frac { 5 y ^ { 4 } } { x ^ { 4 } + y ^ { 5 } + z ^ { 6 } } j + \frac { 6 z ^ { 5 } } { x ^ { 4 } + y ^ { 5 } + z ^ { 6 } } k\)
• C) \(\nabla f = \frac { 1 } { x ^ { 4 } } i + \frac { 1 } { y ^ { 5 } } j + \frac { 1 } { z ^ { 6 } } k\)
• D) \(\nabla f = \frac { 4 } { x ^ { 4 } } i + \frac { 5 } { y ^ { 5 } } j + \frac { 6 } { z ^ { 6 } } k\)

Recognize the concept of rank-order personality consistency.

Know the variations in personality traits and disorders across the lifespan.

Acknowledge the influence of physical and experiential factors on personality development.

Understand key concepts and theories related to personality development.

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