यदि `y=a^(x^(a^(x^(...oo))))`, तो सिद्ध कीजिए कि `(dy)/(dx)=(y^(2)logy)/(x(1-ylogxlogy))`

यदि `y=a^(x^(a^(x^(...oo))))`, तो सिद्ध कीज�

1.	यदि `y=a^(x^(a^(x^(...oo))))`, तो सिद्ध कीजिए कि `(dy)/(dx)=(y^(2)logy)/(x(1-ylogxlogy))`
Answer» `y=a^(x^(a^(x^(...oo))))`, `y=a^(x^(y))` `rArr" "logy=loga^(x^(y))=x^(y).loga` `rArr" "log(logy)=logx^(y)+log(loga)` `" "=ylogx+log(loga)` दोनों पक्षों का x के सापेक्ष अवकलन करने पर `(1)/(ylogy)(dy)/(dx)=(y)/(x)+logx.(dy)/(dx)+0` `rArr" "((1)/(ylogy)-logx)(dy)/(dx)=(y)/(x)` `rArr" "((1-ylogxlogy))/(ylogy).(dy)/(dx)=(y)/(x)` `rArr" "(dy)/(dx)=(y^(2)logy)/(x(1-ylogxlogy))` यही सिद्ध करना था ।