Find `(dy)/(dx)`, when: `y=sin(x^(x))`

1.	Find `(dy)/(dx)`, when: `y=sin(x^(x))`
Answer» Correct Answer - `[cos(x^(x))]x^(x)(1+logx)` Let `x^(x)=t`. Then, `logt=xlogx rArr(1)/(t).(dt)/(dx)=x.(1)/(x)+logx.1` `rArr(dt)/(dx)=t[1+logx]=x^(x)(1+logx).` `thereforey=sint rArr(dy)/(dt)=cost=cosx^(x).` `therefore(dy)/(dx)=((dy//dt))/((dx//dt))=[cos(x^(x))]x^(x)(1+logx).`

Discussion

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