For and , let . Determine…

MATHEMATICS · Single correct · AP · Calculus AB · Differentiation: Definition and Fundamental Properties · Differentiation: Definition and Fundamental Properties

Problem

For x≠0x\neq0 and cos⁡x≠0\cos x \neq0, let y=x2+3x+2xcos⁡xy=\dfrac{x^{2}+3x+2}{x\cos x}. Determine dydx\dfrac{dy}{dx}. (a) (x2−2)cos⁡x−x(x2+3x+2)sin⁡xx2cos⁡2x\dfrac{(x^{2}-2)\cos x - x(x^{2}+3x+2)\sin x}{x^{2}\cos^{2}x} (b) (x2−2)cos⁡x+x(x2+3x+2)sin⁡xx2cos⁡2x\dfrac{(x^{2}-2)\cos x + x(x^{2}+3x+2)\sin x}{x^{2}\cos^{2}x} (c) (x2−2)cos⁡x+(x2+3x+2)sin⁡xx2cos⁡2x\dfrac{(x^{2}-2)\cos x + (x^{2}+3x+2)\sin x}{x^{2}\cos^{2}x} (d) (−x2+2)cos⁡x−x(x2+3x+2)sin⁡xx2cos⁡2x\dfrac{(-x^{2}+2)\cos x - x(x^{2}+3x+2)\sin x}{x^{2}\cos^{2}x}

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