Question

if x log y - y log x = 2 find dy/dx

Answer 1

Step-by-step explanation:

We have,

$x log(y) - y log(x) = 2$

$\implies log(y) + \frac{x}{y} \frac{dy}{dx} - \frac{y}{x} - log(x ) . \frac{dy}{dx} = 0$

$\implies log(y) - \frac{y}{x} + (\frac{x}{y} - log(x ) )\frac{dy}{dx} = 0$

$\implies (\frac{x}{y} - log(x ) )\frac{dy}{dx} = \frac{y}{x} - log(y)$

$\implies \frac{dy}{dx} = \frac{ \frac{y}{x} - log(y)}{ \frac{x}{y} - log(x ) }$