Find dy/dx by implicit differentiation. x² - 8xy + y² = 8

Solution:

Given x² - 8xy + y² = 8

Implicit function means we cannot write y in terms of x

Implicit differentiation means differentiating w.r.t one variable keeping the other constant

2x - 8xdy/dx - 8y + 2ydy/dx = 0

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

dy/dx = 8y - 2x / 2y - 8x

= 2(4-x)/2(y-4x)

dy/dx= (4-x)/(y-4x)

Find dy/dx by implicit differentiation. x² - 8xy + y² = 8

Summary:

Given x² - 8xy + y² = 8 , dy/dx by implicit differentiation is dy/dx = (4-x)/(y-4x)