find the slope of the tangent line to the curve at the point (1,1)?

Question

X^2+3XY-Y=3

Answer 1

x^2 +3xy -y = 3
x^2 -3 = (1 - 3x)y
y = (x^2)/(1 - 3x)
Use the quotient rule:
dy/dx = [(1 - 3x)(2x) - (x^2 - 3)]/(1 - 3x)^2
dy/dx = (-9x^2 + 2x - 9)/(1 - 3x)^2
Evaluate at x = 1:
dy/dx = (-9 + 2 - 9)/(-2)^2 = 1/2