if-y-x-1-x-1-x-1-x-find-y-

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

i f y = x + \frac{1}{x + \frac{1}{x + \frac{1}{x} ._{._{._{._{.}}}}}} f i n d y^{^{'}}

Answered by mindispower last updated on 01/Jan/22

y = x + \frac{1}{y}

\Rightarrow y^{'} = - \frac{y^{'}}{y^{2}} + 1

y^{'} = \frac{y^{2}}{y^{2} + 1}

Commented by mkam last updated on 01/Jan/22

p u t y^{^{'}} = \frac{y}{2 y - 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^{'} = \frac{1}{2} + \frac{x}{2 \sqrt{x^{2} + 4}}

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