Find the simplified derivative of .

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

Problem

Find the simplified derivative of f(x)=(x2+3x)sin⁡xx3f(x)=\dfrac{(x^{2}+3x)\sin x}{x^{3}}. (a) x(x+3)sin⁡x−(x+6)cos⁡xx3\dfrac{x(x+3)\sin x-(x+6)\cos x}{x^{3}} (b) x(x+3)cos⁡x+(x+6)sin⁡xx3\dfrac{x(x+3)\cos x+(x+6)\sin x}{x^{3}} (c) x(x+3)cos⁡x−(x+6)sin⁡xx3\dfrac{x(x+3)\cos x-(x+6)\sin x}{x^{3}} (d) (x+3)cos⁡x−(x+6)sin⁡xx3\dfrac{(x+3)\cos x-(x+6)\sin x}{x^{3}}

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