AP Calculus ABeasymcq1 pt

If f(x)=tan(5x)f(x)=\tan(5x), then f(x)=f'(x)=

A.sec2(5x)\sec^2(5x)
B.5sec2x5\sec^2 x
C.5sec2(5x)5\sec^2(5x)
D.5tan(5x)sec(5x)5\tan(5x)\sec(5x)

Explanation

Core Concept

Since tanu=sec2u\tan' u=\sec^2 u, the chain rule gives sec2(5x)5\sec^2(5x)\cdot 5. The inner derivative of 5x5x is 5.

Correct Answer

C5sec2(5x)5\sec^2(5x)

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