#### Answer

$\frac{dy}{dx}=\frac{1}{2y(x+1)^2}$

#### Work Step by Step

Take the derivative of the equation on each side separately. Apply chain rule when differentiating the "y" variables since we are differentiating with respect to x:
$2y\frac{dy}{dx}=\frac{(x+1)(1)-(x)(1)}{(x+1)^2}$
$2y\frac{dy}{dx}=\frac{x+1-x}{(x+1)^2}$
$2y\frac{dy}{dx}=\frac{1}{(x+1)^2}$
Move all terms with dy/dx to one side of the equation, and isolate dy/dx:
$\frac{dy}{dx}=\frac{1}{2y(x+1)^2}$