$\text { Find } \mathrm { f } _ { \mathbf { x } } , \mathrm { f } _ { \mathbf { y } } \text {, and } \mathrm { f } _ { \mathbf { Z } }$

question 346

Multiple Choice

$\text { Find } \mathrm { f } _ { \mathbf { x } } , \mathrm { f } _ { \mathbf { y } } \text {, and } \mathrm { f } _ { \mathbf { Z } }$
- $$f ( x , y , z ) = \frac { z } { \sqrt { x + y ^ { 2 } } }$$

• A) \(f _ { x } = \frac { z } { 2 \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { y } = \frac { y z } { \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { z } = \frac { 1 } { \sqrt { x + y ^ { 2 } } }\)
• B) \(f _ { x } = - \frac { z } { 2 \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { y } = \frac { y z } { \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { z } = - \frac { 1 } { \sqrt { x + y ^ { 2 } } }\)
• C) \(f _ { x } = \frac { z } { 2 \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { y } = - \frac { y z } { \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { z } = \frac { 1 } { \sqrt { x + y ^ { 2 } } }\)
• D) \(f _ { x } = - \frac { z } { 2 \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { y } = - \frac { y z } { \left( x + y ^ { 2 } \right) ^ { 3 / 2 } } ; f _ { z } = \frac { 1 } { \sqrt { x + y ^ { 2 } } }\)

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Definitions:

Embryonic Differentiation

Embryonic differentiation is the process during embryonic development in which unspecialized stem cells give rise to specialized cells, forming various tissues and organs.

Apical Meristems

Regions at the tips of roots and shoots in plants where cells actively divide, allowing for elongation and growth.

Dermal Tissues

Plant tissues that make up the outer layer of a plant, providing protection and aiding in gas exchange.

Vascular Tissues

The complex tissues in plants responsible for conducting water, nutrients, and food throughout the organism, consisting mainly of xylem and phloem.