Use implicit differentiation to find the slope of the tangent line at the point (2,-4) on the curve 2x^2-3y^2=5xy

Answer 1

2x^2 - 3y^2 = 5xy

4x - 6y y' = 5x y' + 5y

4x - 5y = 5x y' + 6y y'

4x - 5y = (4x + 6y) y'

(4x - 5y)/(4x+6y) = y'

the slope is

(4 * 2 - 5 * -5) / ( 4 * 2 - 6 * -4) = y'

( 8 - -25)/( 8 - -24) = y'

33/32 = y'