Use implicit differentiation to find dy/dx y= x+8/y-8

Question

Dy/dx=?

Answer 1

Separate x and y

y = (x+8)/(y-8)

y(y-8) = x+8

y²-8y = x+8

Differentiate both sides w.r.t x and solve for dy/dx

(2y-8)(dy/dx) = 1

dy/dx = 1/(2y-8)

Remember that in implicit differentiation that "y" is treated as a constant, so dy/dx needs to be added on like in the previous steps, hope this helped!