AP Calculus ABeasymcq1 pt

If f(x)=sec(4x)f(x)=\sec(4x), then f(x)=f'(x)=

A.sec(4x)tan(4x)\sec(4x)\tan(4x)
B.4secxtanx4\sec x\tan x
C.4sec2(4x)4\sec^2(4x)
D.4sec(4x)tan(4x)4\sec(4x)\tan(4x)

Explanation

Core Concept

Since secu=secutanu\sec' u=\sec u\tan u, the chain rule gives sec(4x)tan(4x)4\sec(4x)\tan(4x)\cdot 4. The inner derivative of 4x4x is 4.

Correct Answer

D4sec(4x)tan(4x)4\sec(4x)\tan(4x)

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