Let for all such that

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

Let h(x)=sin⁡x1+cos⁡xh(x)=\dfrac{\sin x}{1+\cos x} for all xx such that cos⁡x≠−1\cos x\neq -1. Which of the following is an equivalent simplified form of h′(x)h'(x)? (a) −11+cos⁡x-\dfrac{1}{1+\cos x} (b) cos⁡x1+cos⁡x\dfrac{\cos x}{1+\cos x} (c) 11+cos⁡x\dfrac{1}{1+\cos x} (d) 1−cos⁡x(1+cos⁡x)2\dfrac{1-\cos x}{(1+\cos x)^2}

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