For differentiable functions and

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

Problem

For differentiable functions x=f(t)x=f(t) and y=g(t)y=g(t), which of the following expressions equals d2ydx2\dfrac{d^{2}y}{dx^{2}} in terms of tt? (a) f′′(t) g′(t)−f′(t) g′′(t)[f′(t)]3\dfrac{f''(t)\,g'(t)-f'(t)\,g''(t)}{[f'(t)]^{3}} (b) g′′(t)f′(t)\dfrac{g''(t)}{f'(t)} (c) g′′(t) f′(t)−g′(t) f′′(t)[f′(t)]3\dfrac{g''(t)\,f'(t)-g'(t)\,f''(t)}{[f'(t)]^{3}} (d) g′′(t) f′(t)−g′(t) f′′(t)[f′(t)]2\dfrac{g''(t)\,f'(t)-g'(t)\,f''(t)}{[f'(t)]^{2}}

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