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

question 59

Multiple Choice

Find the requested partial derivative.
- $( \partial w / \partial x ) _ { y }$ if $w = x ^ { 3 } + y ^ { 3 } + z ^ { 3 } + 18 x y z$ and $z = x ^ { 2 } + y ^ { 2 }$

• A) \(3 x \left( 3 x + 2 z ^ { 2 } \right) + 18 y \left( 2 x ^ { 2 } + 3 z \right)\)
• B) \(3 x \left( x + 2 z ^ { 2 } \right) + 18 y \left( 2 x ^ { 2 } + z \right)\)
• C) \(3 x \left( x + 2 z ^ { 2 } \right) + 18 y \left( 2 x ^ { 2 } + 3 z \right)\)
• D) \(3 x \left( 3 x + 2 z ^ { 2 } \right) + 18 y \left( 2 x ^ { 2 } + z \right)\)

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Definitions:

Average Total Cost

Total cost divided by the number of units produced. It is sometimes called per-unit cost.

Long Run

A time period long enough to allow the firm to vary all of its factors of production.

Price Searchers

Firms that face a downward-sloping demand curve for their product. The amount the firm is able to sell is inversely related to the price it charges.

Price Takers

Sellers who must take the market price in order to sell their product. Because each price taker's output is small relative to the total market, price takers can sell all their output at the market price, but they are unable to sell any of their output at a price higher than the market price.