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) \(\nabla f = x ^ { 5 } e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } } i + y ^ { 4 } e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } } j + z ^ { 6 } e ^ { x ^ { 6 } + y ^ { 5 } + z ^ { 7 } } \mathbf { k }\)

Know the anatomical and functional aspects of cranial nerves and their role in the body.

Distinguish between congenital and acquired neurological conditions.

Understand the etiology and implications of increased cerebrospinal fluid in the brain.

Recognize terminology and definitions specific to neurology and neurosurgery.

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Definitions:

Dictyostelium

A genus of slime molds that are used as model organisms in molecular biology and genetics.

Mitochondria

The organelles within cells that generate most of the cell's supply of ATP, used as a source of chemical energy, and involved in a range of other processes including signaling and cellular differentiation.

Nuclei

Membrane-bound organelles found in eukaryotic cells that contain most of the cell's genetic material.

Chloroplasts

Organelles found in plant and algal cells responsible for photosynthesis, containing the pigment chlorophyll.