If for differentiable functions and with

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

Problem

If m(t)=g′(t)f′(t)m(t)=\dfrac{g'(t)}{f'(t)} for differentiable functions ff and gg with f′(t)≠0f'(t)\neq0, which of the following is the correct expression for dmdt\dfrac{dm}{dt}? (a) f′(t)g′′(t)+g′(t)f′′(t)[f′(t)]2\displaystyle \frac{f'(t)g''(t)+g'(t)f''(t)}{[f'(t)]^{2}} (b) g′(t)f′′(t)−f′(t)g′′(t)[f′(t)]2\displaystyle \frac{g'(t)f''(t)-f'(t)g''(t)}{[f'(t)]^{2}} (c) f′(t)g′′(t)−g′(t)f′′(t)[f′(t)]2\displaystyle \frac{f'(t)g''(t)-g'(t)f''(t)}{[f'(t)]^{2}} (d) g′′(t)f′(t)\displaystyle \frac{g''(t)}{f'(t)}

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