If y = logn x, where logn means log log log (repeated n times), then x log x log2x log3x - Maths - Continuity and Differentiability

Question

If y = logn x, where logn means log log
log (repeated n times), then x log x log2x
log3x logn-1
x logn x dy/dx is equal to???

Vipin Verma · Accepted Answer

y = lognx, here lognx = log(log(log upto n times)So if we take n =
2 then y = log2x = log(logx)So dydx= 1logx ×1x = 1log1x
×1xIf we take n = 3, then y = log3x =
log(log(logx)dydx=1log(logx)×1logx×1x =
1log2x×1log1x×1x Similarly if n =n , theny = lognxSo
dydx=1log(n-1)x×1logn-2x 1log1x×1x (1)So x log1x log2x
log3x logn-1x lognx×dydx =lognx (Ans) (using (1)) as other
terms cancels out

If y = logn x, where logn means log log log (repeated n times), then x log x log2x log3x. logn-1 x logn x dy/dx is equal to???

If y = logⁿ x, where logⁿ means log log log (repeated n times), then x log x log²x log³x. log^n-1

x logⁿ x dy/dx is equal to???