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Question Number 26983 by chernoaguero@gmail.com last updated on 31/Dec/17

$$\mathrm{Find}\frac{\mathrm{dy}}{\mathrm{dx}}$$$${\mathrm{x}}^{\mathrm{y}}={\mathrm{y}}^{\mathrm{x}}$$

Answered by mrW1 last updated on 31/Dec/17

$$y\ln x=x\ln y$$$$y^{\prime }\ln x+\frac{y}{x}=\ln y+\frac{x}{y}{y}^{\prime }$$$$(\frac{x}{y}-\ln x)y^{\prime }=\frac{y}{x}-\ln y$$$$\frac{dy}{dx}=y^{\prime }=\frac{\frac{y}{x}-\ln y}{\frac{x}{y}-\ln x}$$

Commented by chernoaguero@gmail.com last updated on 31/Dec/17

$$\mathrm{Good}\mathrm{thankx}\mathrm{u}\mathrm{sir}$$

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