Find the Derivative of the Function $$y = 3 \sin ^ { - 1 } \left( x ^ { 2 } \right)$$

question 14

Multiple Choice

Find the derivative of the function. $$y = 3 \sin ^ { - 1 } \left( x ^ { 2 } \right)$$

• A)
• \(y ^ { t } = \frac { 6 x } { \sqrt { 1 + x ^ { 4 } } }\)
• B)
• \(y ^ {t } = \frac { x } { \sqrt { 1 - x ^ { 2 } } }\)
• C)
• \(y ^ { t } = \frac { 6 x } { \sqrt { 1 - x ^ { 4 } } }\)
• D)
• \(y ^ { t } = \frac { 6 x } { \sqrt { 1 - x ^ { 2 } } }\)
• E) None of these

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Definitions:

Sliding Clutches

Sliding clutches are components in a transmission that allow for the engagement and disengagement of gears during the gear shifting process.

Twin-countershaft

A design feature in transmissions where two countershafts work in parallel to distribute the load and allow for more gear ratios, enhancing performance and durability.

Transmission Assembly

A collection of components that transmit power from a vehicle's engine to its wheels, enabling the vehicle to move.

Range Slipout

A condition where a transmission unexpectedly slips out of a selected drive range into neutral or another range, often due to mechanical failure.