Question

If x^y = y^x, then find `dy/dx`

Answer 1

x^y = y^x

y log x = x log y

By differentiating on both sides,

`y * 1/x + log x dy/dx = x * 1/y dy/dx + log y`

`dy/dx(logx - x/y) = log y - y/x`

`dy/dx = (log y - y/x)/(log x - x/y)`