Differentiate `x^(x)` w.r.t. x.

1.	Differentiate `x^(x)` w.r.t. x.
Answer» Let `y=x^(x)." …(i)"` Taking logarithm on both sides of (i), we get `logy=x log x." …(ii)"` On differentiating both sides of (ii) w.r.t. x, we get `(1)/(y).(dy)/(dx)=x.(d)/(dx)(logx)+logx.(d)/(dx)(x)` `=(x.(1)/(x)+logx.1)=(1+logx)` `rArr(dy)/(dx)=y(1+logx)` `rArr (dy)/(dx)=x^(x)(1+logx).`

Discussion

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