find y'(x) if x^y=y^x

2 answers

x^y=y^x --->

y log(x) = x log(y) ----->

log(x) dy + y/x dx =
log(y) dx + x/y dy ---->

[log(x) - x/y] dy = [log(y) - y/x] dx

---->

dy/dx = [log(y) - y/x]/[log(x) - x/y]
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