Menu Close

xy-3-y-Find-dy-dx-




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

Leave a Reply

Your email address will not be published. Required fields are marked *