Implicit Differentiation
posted by jasmineT .
Use implicit differentiation to find the slope of the tangent line to the curve
y/x+6y=x^2–6 at the point (1,–5/31) .
Again i think i'm messing up with the algebra here. I used quotient rule to get
[(x+6y)(y')(y)(1+6y')]/(x+6y)^2=2x
I don't know how to go from here to find the m. Please help :)

Your derivative equation looks good.
sub in x=1 and y = 5/31 into that derivative equation, then solve it for y'
that will be your m
Good luck with that messy arithmetic. 
I got y'=(2x+x^2+12yx+6y^2y)/(x+6y+6)
But when i plugged in the numbers it came out right... do you think the equation is wrong or i just typed in the numbers wrong?
BTW thanks for replying! 
using your [(x+6y)(y')(y)(1+6y')]/(x+6y)^2=2x
we can continue
xy' + 6yy'  y  6yy' = 2x
xy'  y = 2x
y' = (2x+y)/x
using the given point:
y' = (2  5/31)/1 = 57/31
y + 5/31 = (57/31)(x1)
31y + 5 = 57x  57
57x  31y = 62
check my arithmetic. 
I did this exactly with this question and i got the wrong answer.
Use implicit differentiation to find the slope of the tangent line to the curve
y/(x+5y)=x^3+5
at the point (x=1, y=6/–29).
But I noticed after "we can continue..."
the denominator was moved to the right side of the equation.. so maybe that's it..?? 
Sorry. I meant the denominator from the quotient rule was never multiplied to the right or so. I don't see it. Where did that portion go?