Which of the following gives the correct derivative of with respect to for ?

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

Problem

Which of the following gives the correct derivative of f(x)g(x)\dfrac{f(x)}{g(x)} with respect to xx for g(x)≠0g(x)\neq 0? (a) f′(x)g(x)+f(x)g′(x)[g(x)]2\dfrac{f'(x)g(x)+f(x)g'(x)}{[g(x)]^{2}} (b) g′(x)f(x)−f′(x)g(x)[g(x)]2\dfrac{g'(x)f(x)-f'(x)g(x)}{[g(x)]^{2}} (c) f′(x)g(x)−f(x)g′(x)[g(x)]2\dfrac{f'(x)g(x)-f(x)g'(x)}{[g(x)]^{2}} (d) f′(x)g(x)−f(x)g′(x)[f(x)]2\dfrac{f'(x)g(x)-f(x)g'(x)}{[f(x)]^{2}}

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