What is the derivative of for ?

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

Problem

What is the derivative of f(x)=arcsec⁡(x)f(x)=\operatorname{arcsec}(x) for ∣x∣>1|x|>1? (a) f′(x)=xx2−1\displaystyle f'(x)=\frac{x}{\sqrt{x^{2}-1}} (b) f′(x)=1xx2−1\displaystyle f'(x)=\frac{1}{x\sqrt{x^{2}-1}} (c) f′(x)=1∣x∣x2−1\displaystyle f'(x)=\frac{1}{|x|\sqrt{x^{2}-1}} (d) f′(x)=11−x2\displaystyle f'(x)=\frac{1}{\sqrt{1-x^{2}}}

Related theory

Browse the problem library