AP Calculus ABhardmcq1 pt

If f(x)=cscxf(x)=\csc x, then f ⁣(π6)=f'\!\left(\frac{\pi}{6}\right)=

A.232\sqrt{3}
B.23-2\sqrt{3}
C.3-\sqrt{3}
D.2-2

Explanation

Core Concept

Here f(x)=cscxcotxf'(x)=-\csc x\cot x. Since cscπ6=2\csc\frac{\pi}{6}=2 and cotπ6=3\cot\frac{\pi}{6}=\sqrt{3}, the value is 23-2\sqrt{3}.

Correct Answer

B23-2\sqrt{3}

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