Use implicit differentiation to find dy/dx without first solving for y

Question

Use implicit differentiation to find dy/dx without first solving for y

3x^2+3x+xy=6

dy/dx

At the given point, find the slope.

dy/dx

-(-3,-4)

Answer 1

3x²+3x+xy=6

Taking the implicit derivative of both sides:

6x+3+xy'+y = 0

y' = (-6x-3-y)/x

slope at (-3-,4) = y'(-3,-4) = (-6(-3)-3-(-4))/-3 = (18-3+4)/-3 = -19/3