Question

Find dy/dx by implicit differentiation xy=6

Answer 1

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

Answer 2

dy/dx = -y/x

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