For parametric equations and with

MATHEMATICS · Single correct · CBSE · Mathematics · Continuity and Differentiability · Continuity and Differentiability

Problem

For parametric equations x=f(t)x=f(t) and y=g(t)y=g(t) with f′(t)≠0f'(t)\neq0, which of the following expressions equals d2ydx2\dfrac{d^{2}y}{dx^{2}}? (a) g′′(t)f′(t)−g′(t)f′′(t)[f′(t)]2\dfrac{g''(t)f'(t)-g'(t)f''(t)}{[f'(t)]^{2}} (b) g′′(t)f′(t)−f′′(t)g′(t)[g′(t)]3\dfrac{g''(t)f'(t)-f''(t)g'(t)}{[g'(t)]^{3}} (c) f′(t)g′′(t)−g′(t)f′′(t)[f′(t)]3\dfrac{f'(t)g''(t)-g'(t)f''(t)}{[f'(t)]^{3}} (d) f′′(t)g′(t)−g′′(t)f′(t)[f′(t)]3\dfrac{f''(t)g'(t)-g''(t)f'(t)}{[f'(t)]^{3}}

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