Find the Gradient Field of the Function A) $\bar { V } = ( 5 + 7 x ) x ^ { 4 } e ^ { 7 x _ { i } } + 3 y ^ { 2 } z ^ { 7 } j + 7 y ^ { 3 } z ^ { 6 } \mathbf { k }$

question 7

Multiple Choice

Find the gradient field of the function.
- $$\mathrm { f } ( \mathrm { x } , \mathrm { y } , \mathrm { z } ) = \mathrm { x } ^ { 5 } \mathrm { e } ^ { 7 \mathrm { x } } + \mathrm { y } ^ { 3 } \mathrm { z } ^ { 7 }$$

• A) \(\bar { V } = ( 5 + 7 x ) x ^ { 4 } e ^ { 7 x _ { i } } + 3 y ^ { 2 } z ^ { 7 } j + 7 y ^ { 3 } z ^ { 6 } \mathbf { k }\)
• B) \(\nabla = ( 1 + x ) x ^ { 4 } e ^ { 7 x _ { i } } + y ^ { 2 } z ^ { 7 } j + y ^ { 3 } z ^ { 6 } k\)
• C) \(\bar { A } = ( 5 + 7 x ) x ^ { 4 } e ^ { 7 x _ { i } } + 3 y ^ { 2 } j + 7 z ^ { 6 } \mathbf { k }\)
• D) \(\overline { \mathrm { f } } = ( 5 + 7 x ) \mathrm { x } ^ { 4 } \mathrm { e } ^ { 7 x _ { i } } + \left( \mathrm { x } ^ { 5 } \mathrm { e } ^ { 7 x } + 3 \mathrm { y } ^ { 2 } \mathrm { z } ^ { 7 } \right) \mathrm { j } + \left( \mathrm { x } ^ { 5 } \mathrm { e } ^ { 7 x } + 7 \mathrm { y } ^ { 3 } \mathrm { z } ^ { 6 } \right) \mathbf { k }\)

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Definitions:

Electron Configuration

The distribution of electrons of an atom or molecule in atomic or molecular orbitals, influencing chemical bonds and properties.

Element

A substance that cannot be broken down into simpler substances by chemical means, consisting of atoms all with the same number of protons.

Electron Configuration

The arrangement of electrons in an atom or molecule within atomic or molecular orbitals.

Electron Configuration

How electrons are distributed within the atomic or molecular orbitals of an atom or molecule.