Find the Derivative of the Function $$y = 3 \cos ^ { - 1 } \left( \sin ^ { - 1 } t \right)$$

question 7

Multiple Choice

Find the derivative of the function. $$y = 3 \cos ^ { - 1 } \left( \sin ^ { - 1 } t \right)$$

• A)
• \[y ^ { t } = - \frac { 3 } { \sqrt { \left( 1 - t ^ { 2 } \right) \left( 1 - \left( \sin ^ { - 1 } ( t ) \right) ^ { 2 } \right) } }\]
• B)
• \[y ^ { t } = - \frac { 3 } { \sqrt { \left( 1 - t ^ { 2 } \right) \left( 1 - \sin ^ { - 1 } ( t ) \right) } }\]
• C)
• \[y ^ { \prime } = - \frac { 3 } { \sqrt { \left( 1 - t ^ { 2 } \right) } }\]
• D)
• \[y ^ { t } = - \frac { 3 } { \sqrt { 1 - \left( \sin ^ { - 1 } ( t ) \right) ^ { 2 } } }\]
• E)
• \[y ^ { t } = - \frac { 3 } { \sqrt { \left( 1 + t ^ { 2 } \right) \left( 1 + \left( \sin ^ { - 1 } ( t ) \right) ^ { 2 } \right) } }\]

---

Definitions:

Marginal Utility

The additional satisfaction or utility gained from consuming one more unit of a good or service.

Total Utility

The overall satisfaction or benefit a person receives from consuming a particular quantity of goods or services.

Income Effect

The alteration in a person's or an economy's earnings and its effect on the amount of a product or service they seek to purchase.

Law of Demand

The principle that there is an inverse relationship between the price of a good and the amount of it consumers are willing to buy, all else being equal.