Question

What is the slope of the line tangent to the curve 3y^2-2x^2=6-2xy at the point (3 2)?

Answer 1

3y² - 2x² = 6 - 2xy
6ydy/dx - 4x = 0 -2xydy/dx
6ydy/dx+2xydy/dx = 4x
(6y+2xy)dy/dx =4x
dy/dx = 4x/ (6y+2xy)
dy/dx| x=3 : = 4(3) /{ 6(2) +2×3×2}
= 12/ {12+12}
=12/24 = 1/2