If , then…

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

Problem

If y=x(log⁡x)log⁡(log⁡x)y = x^{(\log x)^{\log(\log x)}} , then dydx\frac{dy}{dx} is (a) yx((ln⁡x)cos⁡x−1+2ln⁡xln⁡(ln⁡x))\frac{y}{x} ((\ln x)^{\cos x - 1} + 2 \ln x \ln(\ln x)) (b) yx(log⁡x)log⁡(log⁡x)(2log⁡(log⁡x)+1)\frac{y}{x} (\log x)^{\log(\log x)} (2 \log(\log x) + 1) (c) yxln⁡x[(ln⁡x)2+2ln⁡(ln⁡x)]\frac{y}{x \ln x} [(\ln x)^2 + 2 \ln(\ln x)] (d) ylog⁡yxlog⁡x[2log⁡(log⁡x)+1]\frac{y \log y}{x \log x} [2 \log(\log x) + 1]

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