A Level

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

Problem

If y=2(x−sin⁡x)3/2xy = \frac{2(x - \sin x)^{3/2}}{\sqrt{x}} , then dydx=\frac{dy}{dx} = (a) 2(x−sin⁡x)3/2x[321−cos⁡x1−sin⁡x−12x]\frac{2(x - \sin x)^{3/2}}{\sqrt{x}} \left[ \frac{3}{2} \frac{1 - \cos x}{1 - \sin x} - \frac{1}{2x} \right] (b) 2(x−sin⁡x)3/2x[321−cos⁡xx−sin⁡x−12x]\frac{2(x - \sin x)^{3/2}}{\sqrt{x}} \left[ \frac{3}{2} \frac{1 - \cos x}{x - \sin x} - \frac{1}{2x} \right] (c) 2(x−sin⁡x)1/2x[321−cos⁡xx−sin⁡x−12x]\frac{2(x - \sin x)^{1/2}}{\sqrt{x}} \left[ \frac{3}{2} \frac{1 - \cos x}{x - \sin x} - \frac{1}{2x} \right] (d) None of these

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