Let for . Which of the following is…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

Let f(x)=x arcsec⁡(3x)f(x)=x\,\operatorname{arcsec}(3x) for x>13x>\frac{1}{3}. Which of the following is f′(x)f'(x)? (a) arcsec⁡(3x)+1x9x2−1\operatorname{arcsec}(3x)+\frac{1}{x\sqrt{9x^{2}-1}} (b) arcsec⁡(3x)+3x9x2−1\operatorname{arcsec}(3x)+\frac{3x}{\sqrt{9x^{2}-1}} (c) arcsec⁡(3x)+19x2−1\operatorname{arcsec}(3x)+\frac{1}{\sqrt{9x^{2}-1}} (d) 1+19x2−11+\frac{1}{\sqrt{9x^{2}-1}}

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