A Level

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

If y=x[(cos⁡x2+sin⁡x2)(cos⁡x2−sin⁡x2)+sin⁡x]+12xy = x \left[ \left( \cos \frac{x}{2} + \sin \frac{x}{2} \right) \left( \cos \frac{x}{2} - \sin \frac{x}{2} \right) + \sin x \right] + \frac{1}{2\sqrt{x}} , then dydx=\frac{dy}{dx} = (a) (1+x)cos⁡x+(1−x)sin⁡x−14xx(1+x)\cos x + (1-x)\sin x - \frac{1}{4x\sqrt{x}} (b) (1−x)cos⁡x+(1+x)sin⁡x+14xx(1-x)\cos x + (1+x)\sin x + \frac{1}{4x\sqrt{x}} (c) (1+x)cos⁡x+(1+x)sin⁡x−14xx(1+x)\cos x + (1+x)\sin x - \frac{1}{4x\sqrt{x}} (d) None of these

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