Find the Derivative of the Function $$y = \frac { 4 - 2 x ^ { 4 } + x ^ { 5 } } { x ^ { 9 } }$$

question 350

Multiple Choice

Find the derivative of the function.
- $$y = \frac { 4 - 2 x ^ { 4 } + x ^ { 5 } } { x ^ { 9 } }$$

• A) \(\frac { d y } { d x } = - \frac { 36 } { x ^ { 10 } } + \frac { 10 } { x ^ { 6 } } - \frac { 4 } { x ^ { 5 } }\)
• B) \(\frac { d y } { d x } = \frac { 36 } { x ^ { 10 } } - \frac { 10 } { x ^ { 6 } } + \frac { 4 } { x ^ { 6 } }\)
• C) \(\frac { d y } { d x } = - \frac { 36 } { x ^ { 8 } } + \frac { 10 } { x ^ { 4 } } - \frac { 4 } { x ^ { 3 } }\)
• D) \(\frac { d y } { d x } = - 36 x ^ { 10 } + 10 x ^ { 6 } - 4 x ^ { 5 }\)

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Definitions:

Equilibrium Price

A market condition where supply meets demand, and there is no inclination for price to change, leading to market balance.

Mutually Beneficial Trades

Exchanges that occur when all parties involved gain benefits or profits from the transaction.

Total Surplus

The sum of consumer surplus and producer surplus in a market, representing the total net benefit to society from trade.

Consumer Surplus

The separation between what consumers envisage paying for a good or service and the amount they actually disburse.