Hello Max!
Find \(\frac{dy}{dx} \) when \(y= x^{y} +y^{x}\)
\(lny=y\times lnx+ x\times lny \)
\(lny-x\times lny=y\times lnx\)
\(lny\times \left(1-x\right)= y\times lnx \)
\(\frac{y}{lny} = \frac{\left(1-x\right) }{lnx} \)
\(y=\frac{lny}{lnx} \times \left(1-x\right) \)
From here I have to capitulate.
To differentiate, I need
y isolated on one side of the equation.
I'm excited about the solution!
Greetings asinus :- ) !