Question Number 69912 by naka3546 last updated on 29/Sep/19
$$\sqrt{{xy}}\:\:+\:\:\mathrm{3}\:\:=\:\:{y} \\ $$$${Find}\:\:\frac{{dy}}{{dx}}\:\:. \\ $$
Answered by MJS last updated on 29/Sep/19
$$\frac{{y}}{\mathrm{2}\sqrt{{xy}}}{dx}+\frac{{x}}{\mathrm{2}\sqrt{{xy}}}{dy}={dy} \\ $$$$\frac{{y}}{\mathrm{2}\sqrt{{xy}}}{dx}=\left(\mathrm{1}−\frac{{x}}{\mathrm{2}\sqrt{{xy}}}\right){dy} \\ $$$$\frac{{y}}{\mathrm{2}\sqrt{{xy}}}{dx}=\frac{\mathrm{2}\sqrt{{xy}}−{x}}{\mathrm{2}\sqrt{{xy}}}{dy} \\ $$$$\frac{{dy}}{{dx}}=\frac{{y}}{\mathrm{2}\sqrt{{xy}}−{x}} \\ $$