Find the Derivative $$y = \sqrt [ 9 ] { x ^ { 2 } } + x ^ { e }$$

question 540

Multiple Choice

Find the derivative.
- $$y = \sqrt [ 9 ] { x ^ { 2 } } + x ^ { e }$$

• A) \(\frac { 2 x ^ { 7 / 9 } } { 9 } + e x ^ { e }\)
• B) \(\frac { 2 } { 9 x ^ { 7 / 9 } } + e x ^ { e }\)
• C) \(\frac { 2 } { 9 x ^ { 7 / 9 } } + e x ^ { e - 1 }\)
• D) \(\frac { 2 x ^ { 7 / 9 } } { 9 } + e x ^ { e - 1 }\)

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Definitions:

Fixed Expenses

Costs that do not fluctuate with the level of production or sales, such as rent, salaries, and insurance premiums.

Variable Expenses

Costs that change in proportion to the activity or volume of production in a business.

Variable Expense Ratio

The proportion of variable expenses to total sales, indicating how variable costs change with changes in sales volume.

Unit Contribution Margin

The difference between the selling price per unit and the variable cost per unit. This margin helps determine how each unit sold contributes to fixed costs and profits.