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Find(dy)/(dx) if x^y=y^x...

Find`(dy)/(dx) if x^y=y^x`

Text Solution

Verified by Experts

The correct Answer is:
`x^(x)(1+ log x)`
`"Let "y=x^(x). Then, y= e^(xlog x).`
Differentiating both sides w.r.t. x, we get
`(dy)/(dx)=e^(x log x)(d)/(dx)(x log x)`
`=x^(x)(log x+ x(1)/(x))" "[becausee^(x log x)=x^(x)]`
`=x^(x)(1+ log x)`
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