Let . Which of the following is…

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

Problem

Let f(x)=(2x−1)(x2+3)cos⁡x exf(x)=(2x-1)(x^{2}+3)\cos x\,e^{x}. Which of the following is f′(x)f'(x)? (a) 2(x2+3)cos⁡x ex+(2x−1)(2x)cos⁡x ex−(2x−1)(x2+3)sin⁡x ex+(2x−1)(x2+3) xcos⁡x ex2(x^{2}+3)\cos x\,e^{x}+(2x-1)(2x)\cos x\,e^{x}-(2x-1)(x^{2}+3)\sin x\,e^{x}+(2x-1)(x^{2}+3)\,x\cos x\,e^{x} (b) 2(x2+3)cos⁡x ex+(2x−1)(2x)cos⁡x ex−(2x−1)(x2+3)sin⁡x ex2(x^{2}+3)\cos x\,e^{x}+(2x-1)(2x)\cos x\,e^{x}-(2x-1)(x^{2}+3)\sin x\,e^{x} (c) 2(x2+3)cos⁡x ex+(2x−1)(2x)cos⁡x ex−(2x−1)(x2+3)sin⁡x ex+(2x−1)(x2+3)cos⁡x ex2(x^{2}+3)\cos x\,e^{x}+(2x-1)(2x)\cos x\,e^{x}-(2x-1)(x^{2}+3)\sin x\,e^{x}+(2x-1)(x^{2}+3)\cos x\,e^{x} (d) 2(x2+3)cos⁡x ex+(2x−1)(2x)cos⁡x ex+(2x−1)(x2+3)sin⁡x ex+(2x−1)(x2+3)cos⁡x ex2(x^{2}+3)\cos x\,e^{x}+(2x-1)(2x)\cos x\,e^{x}+(2x-1)(x^{2}+3)\sin x\,e^{x}+(2x-1)(x^{2}+3)\cos x\,e^{x}

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