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

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

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

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)

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)

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

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

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

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

If y=x^(y^(x)) , prove that, (dy)/(dx)=(y log y(1+x logx log y))/(x logx(1-x logy)) .