Use implicit differentiation to find the slope of the tangent line to the curve 4xy^3+3xy=14 at the point (2,1)

I got 1/30..
can someone check my answer? :)

Question

Use implicit differentiation to find the slope of the tangent line to the curve 4xy^3+3xy=14 at the point (2,1)

I got 1/30.. 
can someone check my answer? :)

anonymous · Answer

4y^3 + 12xy^2y' + 3y + 3xy' = 0
(12xy^2+3x)y'=-4y^3-3y
y'=(-y^3-3y)/(12xy^2+3x)
(2,1) => (x,y)
y' = (-1-3)/(12(2)(1)+3(2)) = -4/30
y' = -2/15

anonymous · Answer

it says that's wrong.

anonymous · Answer

y'=(-y^3-3y)/(12xy^2+3x)  this part is copied down wrong. 
should be y'=(-4y^3-3y)/(12xy^2+3x) 
If you follow my work, you'll notice that I dropped the 4 before the y^3.
This changes the answer to -7/30

anonymous · Answer

ohhh i get! I had my negative and plus signs messed up when I did it.. Thanks!

anonymous · Answer

happens all the time. After years of calculus, i still make the mistake of missing a coefficient in a previous equation

anonymous · Answer

I had -(3y+4y^3)/(12xy^2+3x)