Your square roots magically disappeared.
Still a square root in there!
Stuck on this problem..
If it were using explicit differentiation, I could do this, but implicitly I'm having some trouble.
What I tried was implicitly differentiating both sides:
(d/dx) [ (4x + 3y)^(1/2) + (2xy)^(1/2) ] = 0
and after differentiating, I ended up with with:
(1/2)*(4x + 3y) * (4+3y') + 2(y + xy') = 0
From there, I plugged in the x,y values (3,8) for x and y, then solved for y', getting..
18 * (4 + 3y') + 2(8 + 3y') = 0
60y' = -88
y = -88/60
which is incorrect.
Am I approaching the problem from the wrong angle?