Find dy/dx by implicit differentiation: x^2-2xy=6?

Answer 1

2x - 2(y+x dy/dx) = 0

2x - 2y - 2x dy/dx = 0

I hope this helps.

Answer 2

You just take the derivative of everything, and add y` where the y is.

(X^2)' -(2XY)' = (6)'
2X - (2Y + 2XY') = 0
^^ use multiplication property ^^
2X - 2Y = 2XY'
^^ get everything on opposite side of Y' ^^
Y' = (X-Y)/X
^^ divide by everything that's not Y' to get it alone, and cancel out the twos ^^

Answer 3

Take d/dx --> 2x - 2y -2xdy/dx = 0

solve

2x dy/dx = 2(x-y) ---> dy/dx = x-y