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Let $y=-\log(\log x)$
$\dfrac{dy}{dx}=-\dfrac{d}{dx}[\log(\log x)]$
$\dfrac{d}{dx}[\log(\log x)]=\dfrac{1}{\log x}\cdot\dfrac{1}{x}$
Therefore, $\dfrac{dy}{dx}=-\dfrac{1}{x\log x}$
Answer: $\boxed{-\dfrac{1}{x\log x}},\; x>1$ ✅
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