Find the Requested Partial Derivative $( \partial \mathrm { w } / \partial \mathrm { z } ) _ { \mathrm { x } }$

question 373

Multiple Choice

Find the requested partial derivative.
- $( \partial \mathrm { w } / \partial \mathrm { z } ) _ { \mathrm { x } }$ at $( \mathrm { x } , \mathrm { y } , \mathrm { z } , \mathrm { w } ) = ( 1,2,9,302 )$ if $\mathrm { w } = \mathrm { x } ^ { 2 } + \mathrm { y } ^ { 2 } + \mathrm { z } ^ { 2 } + 12 \mathrm { xyz }$ and $\mathrm { z } = \mathrm { x } ^ { 3 } + \mathrm { y } ^ { 3 }$

• A) \(\frac { 308 } { 3 }\)
• B) \(\frac { 154 } { 3 }\)
• C) 154
• D) 77

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Definitions:

Total Product Curve

A graphical representation showing how the total quantity of output produced by a firm varies with the quantity of a single variable input, holding other inputs constant.

Average Total Cost Curve

A graph that represents the total cost of production (fixed and variable costs combined) divided by the quantity of output produced, at various levels of output.

Diffusion

The spread of an innovation through its widespread imitation.