If $x ^ { 5 } y = 3 e ^ { x + y } , \text { find } d y / d x$

question 99

Multiple Choice

If $x ^ { 5 } y = 3 e ^ { x + y } , \text { find } d y / d x$

• A) \(\frac { d y } { d x } = \frac { 3 e ^ { x + y } - 5 x ^ { 5 } y } { x ^ { 5 } + 3 e ^ { x + y } }\)
• B) \(\frac { d y } { d x } = \frac { 3 e ^ { x + y } - 5 x ^ { 4 } y } { x ^ { 5 } - 3 e ^ { x + y } }\)
• C) \(\frac { d y } { d x } = \frac { 3 e ^ { x + y } + x ^ { 4 } y } { x ^ { 5 } - 3 e ^ { x + y } }\)
• D) \(\frac { d y } { d x } = \frac { e ^ { x + y } - 5 x ^ { 4 } y } { x ^ { 5 } - e ^ { x + y } }\)
• E) \(\frac { d y } { d x } = \frac { 3 e ^ { x + y } + x ^ { 5 } y } { x ^ { 5 } - e ^ { x + y } }\)

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Definitions:

Fixed Costs

Expenses that remain constant regardless of the amount of products made or sold, including rent, wages, and insurance premiums.

Differential Analysis

A decision-making technique that involves comparing the costs and benefits of alternative actions.

Accumulated Depreciation

The total amount of depreciation expense that has been recorded against a fixed asset up to a specific date, reflecting its wear and use over time.

Salvage Value

The estimated residual value of an asset at the end of its useful life, often considered in depreciation calculations.