Find the Derivative Of $f ( x ) = x ^ { 2 } \cos x$

question 60

Multiple Choice

Find the derivative of $f ( x ) = x ^ { 2 } \cos x$ .

• A)2x cos x
• B) \(2 x \cos x - x ^ { 2 } \sin x\)
• C) \(- 2 x \sin x\)
• D) \(2 x \cos x + x ^ { 2 } \sin x\)
• E) \(2 x \sin x\)
• F) \(3 x ^ { 2 } \cos \left( x ^ { 3 } \right)\)
• G) \(- x ^ { 2 } \sin x\)
• H)None of the above

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Definitions:

Intake Valves

Mechanical components in an engine that open and close to allow the mixture of air and fuel into the combustion chamber for ignition.

Exhaust Valves

Components in an engine that open to allow exhaust gases to exit the combustion chamber after the power stroke.

DOHC

Stands for Dual Overhead Camshaft, a design in internal combustion engines where two camshafts are used to control the valves for improved performance.

Internal Combustion Engines

Engines that generate mechanical power by burning a fuel-air mixture within combustion chambers to create high-pressure gases that drive movement.