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

question 377

Multiple Choice

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

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

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Definitions:

Balanced Equation

An equation in chemistry that shows the same number of atoms of each element in the reactants and products, maintaining mass conservation.

Ethanol

A volatile, flammable, colorless liquid alcohol, used as a solvent and in the manufacture of organic chemicals and biofuels.

Methanol

A simple alcohol with the formula CH₃OH, used as a solvent, antifreeze, fuel, and as feedstock for chemical synthesis.

Balanced Equation

A chemical equation in which the number of atoms for each element is the same on both the reactant and product sides.