To simplify while finding

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

Problem

To simplify sin⁡(x+h)−sin⁡xh\dfrac{\sin(x+h)-\sin x}{h} while finding ddx(sin⁡x)\dfrac{d}{dx}(\sin x), which rearrangement correctly prepares the expression for taking the limit h→0h\to 0? (a) sin⁡x(1−cos⁡h)+cos⁡xsin⁡hh\displaystyle\frac{\sin x(1-\cos h)+\cos x\sin h}{h} (b) sin⁡x(cos⁡h−1)+cos⁡xsin⁡hh\displaystyle\frac{\sin x(\cos h-1)+\cos x\sin h}{h} (c) cos⁡x(cos⁡h−1)+sin⁡xsin⁡hh\displaystyle\frac{\cos x(\cos h-1)+\sin x\sin h}{h} (d) sin⁡xcos⁡h+cos⁡xsin⁡hh\displaystyle\frac{\sin x\cos h+\cos x\sin h}{h}

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