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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