Home
Class 12
MATHS
If y=a^x^a^x^...^(((((oo))))) , then pr...

If `y=a^x^a^x^...^(((((oo)))))` , then prove that `(dy)/(dx)=(y^2(log)_e y)/(x(1-y(log)_e x(log)_e y)`

Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

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

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

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

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

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

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

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