For differentiable functions and with

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

Problem

For differentiable functions u(x)u(x) and v(x)v(x) with v(x)≠0v(x)\neq 0, which of the following equals ddx(u(x)v(x))\dfrac{d}{dx}\Big(\dfrac{u(x)}{v(x)}\Big)? (a) u′(x)v(x)−u(x)v′(x)v(x)\dfrac{u'(x)v(x)-u(x)v'(x)}{v(x)} (b) u′(x)v(x)−u(x)v′(x)[v(x)]2\dfrac{u'(x)v(x)-u(x)v'(x)}{[v(x)]^{2}} (c) u′(x)v(x)+u(x)v′(x)[v(x)]2\dfrac{u'(x)v(x)+u(x)v'(x)}{[v(x)]^{2}} (d) u(x)v′(x)−u′(x)v(x)[v(x)]2\dfrac{u(x)v'(x)-u'(x)v(x)}{[v(x)]^{2}}

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