I'm having trouble with this problem:

Solve using implicit differentiation

$\displaystyle x\sqrt{y+1}=xy+1$

$\displaystyle x\cdot\frac{1}{2}(y+1)^-^\frac{1}{2}\cdot(1)=xy+1$

$\displaystyle x\cdot\frac{1}{2}\cdot\frac{1}{\sqrt{y+1}}=xy+1$

$\displaystyle \frac{x}{2\sqrt{y+1}}=xy+1$

Am I heading in the right direction? Where do I go from here?