Let . Which statement best describes the pattern of the th derivative…

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

Let f(x)=sin⁡xf(x)=\sin x. Which statement best describes the pattern of the nnth derivative f(n)(x)f^{(n)}(x)? (a) The derivatives alternate only between sin⁡x\sin x and cos⁡x\cos x without sign changes. (b) The sequence of derivatives repeats every three derivatives in the order sin⁡x,  cos⁡x,  −sin⁡x\sin x,\;\cos x,\;-\sin x. (c) The sequence of derivatives repeats every four derivatives in the order sin⁡x,  cos⁡x,  −sin⁡x,  −cos⁡x\sin x,\;\cos x,\;-\sin x,\;-\cos x. (d) The sequence of derivatives repeats every four derivatives in the order sin⁡x,  −cos⁡x,  −sin⁡x,  cos⁡x\sin x,\;-\cos x,\;-\sin x,\;\cos x.

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