Which of the following gives in terms of derivatives of and ?

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

Problem

Which of the following gives d2dx2[f(x)g(x)]\dfrac{d^{2}}{dx^{2}}\big[f(x)g(x)\big] in terms of derivatives of ff and gg? (a) f′′(x)g′(x)+f′(x)g′′(x)f''(x)g'(x)+f'(x)g''(x) (b) 2f′(x)g′(x)2f'(x)g'(x) (c) f′′(x)g(x)+2f′(x)g′(x)+f(x)g′′(x)f''(x)g(x)+2f'(x)g'(x)+f(x)g''(x) (d) f′′(x)g(x)+f′(x)g′(x)+f(x)g′′(x)f''(x)g(x)+f'(x)g'(x)+f(x)g''(x)

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