Find the slope of the tangent to the curve

Question

 Find the slope of the tangent to the curve y^2=x^2/(xy−14)  at (6,3)

dy/dx=

Answer 1

xy³ - 14y² = x²

Implicit differentiation:

y³ + 3xy²dy/dx - 28ydy/dx = 2x Now plug in (6,3) and solve.

27 + 162 dy/dx - 84 dy/dx = 12

78 dy/dx = - 15

dy/dx = - 15/78