For a differentiable function

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

Problem

For a differentiable function u(x)≠0u(x)\neq 0, which of the following expressions equals ddx[ln⁡∣u(x)∣]\dfrac{d}{dx}\bigl[\ln|u(x)|\bigr]? (a) u′(x) ln⁡∣u(x)∣u'(x)\,\ln|u(x)| (b) 1u(x)\dfrac{1}{u(x)} (c) u′(x)u(x)\dfrac{u'(x)}{u(x)} (d) ln⁡∣u′(x)∣\ln|u'(x)|

Related theory

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