Answer
$\frac{dy}{dx}=\frac{1}{y(x+1)^2}$
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:
$2y\times\frac{dy}{dx}=\frac{(x+1)(1)-(x-1)(1)}{(x+1)^2}$
$2y\times\frac{dy}{dx}=\frac{x+1-x+1}{(x+1)^2}$
$2y\times\frac{dy}{dx}=\frac{2}{(x+1)^2}$
Isolate dy/dx:
$\frac{dy}{dx}=\frac{1}{y(x+1)^2}$
