Find dy/dx by implicit differentiation. 8 cos x sin y = 6

8sin (x) cos (y) = 6

Take derivative with respect to x. Since y is a function of x, take the derivative for y as well but it is multiplied by dy/dx

chain rule

8cos (x) cos (y) - 8sin (x) sin (y) (dy/dx) = 0

solve for dy/dx

8cos (x) cos (y) = 8sin (x) sin (y) (dy/dx)

[8cos (x) cos (y) ]/[8sin (x) sin (y) ] = dy/dx

simplify

cot (x) cot (y) = dy/dx