Question 1186078
<br>
{{{y^2=b^3/(2x+b)}}}
{{{y^2=b^3(2x+b)^(-1)}}}<br>
Use implicit differentiation.<br>
{{{2y(dy/dx)=-2b^3(2x+b)^(-2)}}}<br>
{{{dy/dx=(-b^3)/(y(2x+b)^2)}}}<br>
Evaluate the derivative at (x,y)=(0,b)<br>
{{{dy/dx=(-b^3)/(b(b^2))=(-b^3)/b^3=-1}}}<br>
ANSWER: -1<br>