Find the Derivative $s = t ^ { 6 } \cos t - 8 t \sin t - 8 \cos t$

question 364

Multiple Choice

Find the derivative.
- $s = t ^ { 6 } \cos t - 8 t \sin t - 8 \cos t$

• A) \(\frac { d s } { d t } = - t ^ { 6 } \sin t + 6 t ^ { 5 } \cos t - 8 t \cos t - 16 \sin t\)
• B) \(\frac { d s } { d t } = - t ^ { 6 } \sin t + 6 t ^ { 5 } \cos t - 8 t \cos t\)
• C) \(\frac { d s } { d t } = - 6 t ^ { 5 } \sin t - 8 \cos t + 8 \sin t\)
• D) \(\frac { d s } { d t } = t ^ { 6 } \sin t - 6 t ^ { 5 } \cos t + 8 t \cos t\)

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Definitions:

Consumer Income

Refers to the total earnings or financial inflow that consumers receive from all sources, affecting their purchasing power and demand for goods and services.

Equilibrium Price

The price at which the quantity of goods supplied matches the quantity of goods demanded in a market, leading to a stable market condition.

Quantity Demanded

The total amount of a good or service that consumers are willing to purchase at a given price level in a specified period.

Quantity Supplied

The level of a commodity or service that manufacturers are eager and capable of providing for purchase at a determined price over an established period.