Question Number 25854 by rita1608 last updated on 15/Dec/17
$${find}\:\frac{{dy}}{{dx}}\:{for}\:{y}=\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}.........}}}} \\ $$
Answered by ibraheem160 last updated on 15/Dec/17
$${y}^{\mathrm{2}} ={x}+{y} \\ $$$$\mathrm{2}{y}\frac{{dy}}{{dx}}=\mathrm{1}+\frac{{dy}}{{dx}} \\ $$$$\frac{{dy}}{{dx}}=\frac{\mathrm{1}}{\mathrm{2}{y}−\mathrm{1}} \\ $$
Commented by rita1608 last updated on 16/Dec/17
$${thanks} \\ $$$$ \\ $$