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

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

A

0

B

-1

C

1

D

not defined

Text Solution

Verified by Experts

The correct Answer is:
C
When x=1`impliesy=1`
Now `y^(x)=x^(y) implies x^("x ln y")=e^("y ln x")`
diff. both sides`implies (dy)/(dx)=(y)/(x)("x log y-y"))/(x(ylogx-x))`
At x=1, y=1 `implies(dy)/(dx)=(1(0-1))/(1(0-1))=1`.
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