For , which of the following best describes for every integer…

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

Problem

For f(x)=sin⁡xf(x)=\sin x, which of the following best describes f(n)(x)f^{(n)}(x) for every integer n≥0n\ge 0? (a) cos⁡(x+nπ2)\cos\bigl(x+\tfrac{n\pi}{2}\bigr) (b) sin⁡(x+nπ)\sin\bigl(x+n\pi\bigr) (c) sin⁡(x+nπ2)\sin\bigl(x+\tfrac{n\pi}{2}\bigr) (d) {sin⁡x,n evencos⁡x,n odd\begin{cases}\sin x,& n\text{ even}\\ \cos x,& n\text{ odd}\end{cases}

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