Question

Diffrentiate x^y=e^(x-y)​

Answer 1

Answer:

${x}^{y} = {e}^{x - y} \\ apply \: log \: on \: both \: sides \\ y log(x) =( x - y) log(e ) \\ y log(x) = x - y \\ differentiate \: wrt \: x \\ \frac{dy}{dx} logx + \frac{y}{x} = 1 - \frac{dy}{dx} \\ \frac{dy}{dx} ( log(x ) + 1) = 1 - \frac{y}{x } \\ \frac{dy}{dx} = \frac{1 - \frac{y}{x} }{ log(x) + 1}$