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Question Number 162809 by mkam last updated on 01/Jan/22

$$ify=x+\frac{1}{x+\frac{1}{x+\frac{1}{x}{.}_{{.}_{{.}_{{.}_{.}}}}}}find{y}^{{}^{\prime }}$$

Answered by mindispower last updated on 01/Jan/22

$$y=x+\frac{1}{y}$$$$\Rightarrow y^{\prime }=-\frac{y^{\prime }}{y^2}+1$$$$y^{\prime }=\frac{y^2}{y^2+1}$$

Commented by mkam last updated on 01/Jan/22

$$put{y}^{{}^{\prime }}=\frac{y}{2y-x}$$

Answered by MJS_new last updated on 01/Jan/22

$$y=x+\frac{1}{y}\Rightarrow y=\frac{x+\sqrt{x^2+4}}{2}\Rightarrow y^{\prime }=\frac{1}{2}+\frac{x}{2\sqrt{x^2+4}}$$

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