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

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:

Maturity Value

The amount payable to an investor at the end of an investment period.

7.5 Years

A timeframe equal to seven and a half years, often used in contexts like finance or project planning.

Compounded Monthly

The process of adding interest to the principal balance of a loan or deposit on a monthly basis, resulting in interest on interest.

Compounded Quarterly

Compound interest that is calculated and added to the principal balance of an investment or loan on a quarterly basis, effectively increasing the amount of interest earned or paid each quarter.