1.

यदि ` y= a^(x^(a^(x)...infty ))` तब सिद्ध कीजिए की ` " "(dy)/(dx) =(y^(2) log y)/(x(1-y log x log y ) )`

Answer» `" "y= a ^(x^(a^(x...infty )))" "(because y= a^(x^(a^(x...infty ))))`
` rArr " "y= a ^(x^(y))`
दोनों पक्षों का लघुगणक लेने पर,
` " "log y= x^(y) log a `
पुनः दोनों पक्षों का लघुगणक लेने पर,
` " "log log y =ylog x+ log log (a) `
दोनों पक्षों का x के सापेक्ष अवकलन करने पर,
`" "(1)/(log y) (dy)/(dx) =y (d)/(dx) log x +log x (dy)/(dx) +0`
या ` " "(1)/(ylog y)(dy)/(dx) =(y)/(x) +log x (dy)/(dx) `
` rArr " "((1)/(ylog y ) -log x) (dy)/(dx) =(y)/(x) `
` rArr " "((1-ylog ylog x )/(y log y ))(dy)/(dx) =(y)/(x)`
` (dy)/(dx) =(y^(2) log y)/(x(1-y log ylog x))`


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