More Implicit Differentiation Help

[communitycoll]

Homework Statement

Find an equation of the tangent line to x^3 + y^3 - 6xy = 0 at the point ((4/3), (8/3))

Homework Equations

I got y = -(8/5)x + (24/5). Is this correct?

The Attempt at a Solution

Lots of algebra involved. Sorry. but I'd rather not type it. I take the derivative of each term and eventually get:

[-3x^2 - 6y] / [3y^2 - 6x].

This simplifies to:

[x^2 + 2y] / [2x - y^2].

I substitute the stuff in appropriately, I get m = -(8 / 5).

Then I do:

y - (8/3) = -(8 / 5)(x - (4/3)).

I ask because Wolfram Alpha disagrees with me:
http://www.wolframalpha.com/input/?...3+++y^3+-+6xy+=+0+at+the+point+((4/3),+(8/3))

 

[Mentallic]

Lots of algebra involved. Sorry. but I'd rather not type it. I take the derivative of each term and eventually get:

[-3x^2 - 6y] / [3y^2 - 6x].

You're off by a sign, it should be

$$\frac{dy}{dx}=\frac{6y-3x^2}{3y^2-6x}$$

 

[communitycoll]

I see. I didn't distribute a "- 6" to a "+ y" properly. Thanks.