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Question Number 159966 by malwaan last updated on 23/Nov/21

$$ay=\sqrt{x+\sqrt{x+\sqrt{x+.....}}}$$$$by=\sqrt{x\sqrt{x\sqrt{x\sqrt{x.....}}}}$$$$find\frac{dy}{dx}$$

Commented by tounghoungko last updated on 23/Nov/21

$$\left(a\right)y=\sqrt{x+y}$$$$y^2-y=x$$$$(2y-1)y^{\prime }=1$$$$y^{\prime }=\frac{1}{2\sqrt{x+\sqrt{x+\sqrt{x+\dots }}}-1}$$

Commented by mr W last updated on 23/Nov/21

$$\left(b\right)$$$$y=x^{\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+...}=x$$$$\frac{dy}{dx}=1$$

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