(x log_(e)x)^(log log_(e)x)

(d)/(dx)log_(7)(log_(7)x)= (a) (1)/(x log_(e)x) (b) (log_(e)7)/(x log_(e)x) (c) (log_(7)e)/(x log_(e)x) (d) (log_(7)e)/(x log_(7)x)

If x^(y) = e^(x - y) prove that (dy)/(dx) = (log_(e)x)/((1 + log_(e)x)^(2)) .

Find the range of f(x)=log_(e)x-((log_(e)x)^(2))/(|log_(e)x|)

y =[ log_(x) (log _(e) x ) ](log _(e) x ) then (dy)/(dx) equals

I=int(log_(e)(log_(e)x))/(x(log_(e)x))dx

The value of 1+(log_(e)x)+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+…infty

if log_(e)(x-1) + log_(e)(x) + log_(e)(x+1)=0 , then

The value of 1+(log_(e)x)+(log_(e)x)^(2)/(2!)+(log_(e)x)^(3)/(3!)+…infty

int [sin(log_(e)x)+cos(log_(e)x)]dx =

if x^(y)=e^(x-y) then prove that (dy)/(dx)=(log_(e)x)/((1+log_(e)x)^(2))