Posted by **Daniela ** on Sunday, November 4, 2012 at 8:04pm.

3x^2+2xy+y^2=2 then the value of dy/dx at x=1 is?

- math -
**Steve**, Monday, November 5, 2012 at 12:58am
using implicit differentiation,

6x + 2y + 2xy' + 2yy' = 0

when x=1, y=-1, so plug them i:

6 - 2 + 2y' - 2y' = 0

Note that there is no solution, so the tangent to the curve is vertical. y' is not defined.

Looking at dx/dy,

6xx' + 2x + 2yx' + 2y = 0

6x' + 2 - 2x' - 2 = 0

4x' = 0

x' = 0

just as we suspected: dx/dy=0, so the slope is vertical.

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