Fermi · Concept Library · Courses · Books · Problems · Simulations · Math Wiki · High School Fermi › Problems Mathematics
Mathematics
Problem If y = x ( log x ) log ( log x ) y = x^{(\log x)^{\log(\log x)}} y = x ( l o g x ) l o g ( l o g x ) d y d x \frac{dy}{dx} d x d y y x ( ( ln x ) cos x − 1 + 2 ln x ln ( ln x ) ) \frac{y}{x} ((\ln x)^{\cos x - 1} + 2 \ln x \ln(\ln x)) x y (( ln x ) c o s x − 1 + 2 ln x ln ( ln x )) y x ( log x ) log ( log x ) ( 2 log ( log x ) + 1 ) \frac{y}{x} (\log x)^{\log(\log x)} (2 \log(\log x) + 1) x y ( log x ) l o g ( l o g x ) ( 2 log ( log x ) + 1 ) y x ln x [ ( ln x ) 2 + 2 ln ( ln x ) ] \frac{y}{x \ln x} [(\ln x)^2 + 2 \ln(\ln x)] x l n x y [( ln x ) 2 + 2 ln ( ln x )] y log y x log x [ 2 log ( log x ) + 1 ] \frac{y \log y}{x \log x} [2 \log(\log x) + 1] x l o g x y l o g y [ 2 log ( log x ) + 1 ] Browse the problem library