AP Calculus ABmediummcq1 pt

If f(x)=sec2(3x)f(x)=\sec^2(3x), then f(x)=f'(x)=

A.2sec2(3x)tan(3x)2\sec^2(3x)\tan(3x)
B.6sec2(3x)tan(3x)6\sec^2(3x)\tan(3x)
C.6sec(3x)tan2(3x)6\sec(3x)\tan^2(3x)
D.6sec2(3x)6\sec^2(3x)

Explanation

Core Concept

The chain rule is applied twice: 2sec(3x)sec(3x)tan(3x)32\sec(3x)\cdot\sec(3x)\tan(3x)\cdot 3. The factors combine to 6sec2(3x)tan(3x)6\sec^2(3x)\tan(3x).

Correct Answer

B6sec2(3x)tan(3x)6\sec^2(3x)\tan(3x)

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