Find dy/dx by implicit differentiation xy=6

dy/dx = - y/x

Step-by-step explanation:

xy = 6

x * dy + y * dx = 0

Subtract y dx from each side

x dy = - y dx

Divide each side by dx

x dy / dx = - y dx/dx

x dy/dx = - y

Divide by x

dy/dx = - y/x

Step-by-step explanation:

Apply the derivative operator d/dx to xy = 6. xy is a product, so we must use the product rule as well as the chain rule.

dy/dx = - y/x

(d/dx) (xy = 6) works out to x (dy/dx) + y (dx/dx) = 0, or just x (dy/dx) + y = 0.

Solving this for dy/dx, we get, first, x (dy/dx) = - y, and then

dy/dx = - y/x