For , the derivative…

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

Problem

For y=(sin⁡x cos⁡x)xy=(\sin x\,\cos x)^{x}, the derivative y′y' is (a) (sin⁡x cos⁡x)x[x (cot⁡x−tan⁡x)] (\sin x\,\cos x)^{x}\big[x\,(\cot x-\tan x)\big] (b) (sin⁡x cos⁡x)x[ln⁡(sin⁡x cos⁡x)+x (cot⁡x−tan⁡x)] (\sin x\,\cos x)^{x}\left[\ln(\sin x\,\cos x)+x\,(\cot x-\tan x)\right] (c) (sin⁡x cos⁡x)x[ln⁡(sin⁡x cos⁡x)+x (cot⁡x+tan⁡x)] (\sin x\,\cos x)^{x}\left[\ln(\sin x\,\cos x)+x\,(\cot x+\tan x)\right] (d) (sin⁡x cos⁡x)x[ln⁡(sin⁡x+cos⁡x)+x (cot⁡x−tan⁡x)] (\sin x\,\cos x)^{x}\left[\ln(\sin x+\cos x)+x\,(\cot x-\tan x)\right]

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