(dy)/(dx)=(2y^(2)csc2x)/(1-y log tan x)

If y=a^(x^(x^(2)*oo)), prove that (dy)/(dx)=(y^(2)log y)/(x(1-y log x*log y))

A: If y = x ^(y) then (dy)/(dx) = (y ^(2))/(x(1- log y )) If y = f (x) ^(y), then (dy)/(dx) = (y ^(2) f '(x))/(f (x) [1- ylog f (x)])= (y ^(2) f'(x))/(f (x) [1- log y])

If y = (cos x)^((cosx)^((cosx)^(-"to"oo) show that (dy)/(dx) = (cdot y^(2) tan x)/(y log cos x -1) .

If x^y = e^(x + y) , show that (dy)/(dx) = (log x - 2)/((1 - log x)^2)

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

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

If y^(x)= e^(y-x) , then prove that (dy)/(dx)= ((1+ log y)^(2))/(log y)

Solve (dy)/(dx)=(y)/(2y log y+y-x).

Find (dy)/(dx):x=a{cos t+(1)/(2)log tan^(2)(t)/(2)} and y=a sin t