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If y^x=x^y then (dy)/(dx) at x=1 in...

If `y^x=x^y` then `(dy)/(dx)` at x=1 in

A

0

B

`-1`

C

1

D

not defined

Text Solution

Verified by Experts

The correct Answer is:
C
When `x=1 rArr y=1`
Now `y^(x)=x^(y)rArr e^(xlny)=e^(ylnx)`
`"Diff . Both sides "rArr (dy)/(dx)=(y(xlogy-y))/(x(ylogx-x))`
`"At "x=1, y=1" "rArr (dy)/(dx)=(1(0-1))/(1(0-1))=1`
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