Question

If xy =1 show that dy/dx=-1/x²​

Answer 1

If xy = 1, then differentiating both sides with respect to x gives

x dy/dx + y = 0

(use the product rule)

Solve for dy/dx :

dy/dx = -y/x

Solve the starting equation for y and substitute that into the derivative.

xy = 1   →   y = 1/x

→   dy/dx = -(1/x)/x = -1/x²