Help please Im having problem with these and Ive tried everything!?: Consider the curve defined by 2y^3+6x^2y-12x^2+6y=

2y36x2y-12x26y

#1

Help please Im having problem with these and Ive tried everything!?: Consider the curve defined by 2y^3+6x^2y-12x^2+6y=1
a) Show that dy/dx = (4x-2xy)/x^2+y^2+1

Answer:

1. Differentiate both sides with respect to x, applying the product rule where appropriate:
6y^2 dy/dx + 12xy + 6x^2 dy/dx - 24x + 6dy/dx = 0
2. Combine terms with dy/dx in them, and move all other terms to the right hand side.
(6y^2 + 6x^2 + 6)dy/dx = 24x - 12xy. Now simplify.
dy/dx = 6(4x - 2xy)/6(y^2 + x^2 + 1

Answer: dy/dx = (4x - 2xy)/x^2 + y^2 + 1.