Aspire Faculty ID #18377 · Topic: AMU MCA 2016 · Just now
AMU MCA 2016

If $x^y = e^{x-y}$, then $\frac{dy}{dx}$ is equal to

Solution

Take log: $y\log x = x - y$ Differentiate: $\frac{dy}{dx}\log x + \frac{y}{x} = 1 - \frac{dy}{dx}$ $\frac{dy}{dx}(1+\log x) = 1 - \frac{y}{x}$ Using $y = \frac{x}{1+\log x}$ Substitute ⇒ $\frac{dy}{dx} = \frac{\log x}{(1+\log x)^2}$
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