1.

यदि ` y= log x^(x) ` तो सिद्ध कीजिए की ` " "(dy)/(dx) =(1+log x )`

Answer» माना ` x^(x) =t " "rArrx log x =log t `
` x*(d)/(dx) (log x )+ log x (d)/(dx) (x) =log t `
` " "x *(1)/(x)+ log x =(1)/(t)(dt)/(dx)`
` rArr " "(dt)/(dx) =x^(x) (1+log x) rArr (dy)/(dx)= (d)/(dx) (log x^(x))`
` rArr " "(dy)/(dx)=(d)/(dt) (log t )(dt)/(dx)= (d)/(dt) (log t ) [x^(x) (1+ log x ) ]`
` " "= (1) /(t) [x ^(x) (1+ log x ) ] =91) /(x^(x)) [ x^(x) (1+log x) ] =1 + log x `


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