If $x^y y^x=100$, then $\frac{d y}{d x}$ is equal to

Question

Professor PC Thomas Classes · Answer

Take $\ln$: $y\ln x + x\ln y = \ln 100$. Implicit diff yields $\frac{dy}{dx} = -\frac{y(y+x\ln x)}{x(x+y\ln y)}$.