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Mathematics · JEE | CONTINUITY AND DIFFERENTIABILITY
हिन्दीWhat is the formula for logarithmic differentiation of \( y = [u(x)]^{v(x)} \)?
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Correct answer · Option B
\( y [ v'(x) \log u(x) + v(x) \frac{u'(x)}{u(x)} ] \)
Explanation
Taking logs gives \( \log y = v(x)\log u(x) \). Differentiating both sides gives \( \frac{1}{y}\frac{dy}{dx} = v'(x)\log u(x) + v(x)\frac{u'(x)}{u(x)} \).
