Find dy/dx by implicit differentiation. x² - 6xy + y² = 6

Solution:

Given x² - 6xy + y² = 6

Implicit function means we cannot write y in terms of x in a given equation

So we need to differentiate partially

2x - 6xdy/dx - 6y + 2ydy/dx = 0

2x = 6xdy/dx - 6y - 2ydy/dx

2x - 6y = 2ydy/dx - 6xdy/dx

2x - 6y = (2y - 6x)dy/dx

dy/dx = 2x - 6y / 6x - 2y

= 2(x - 3y)/2(3x - y)

=(x - 3y)/(3x - y)

Find dy/dx by implicit differentiation. x² - 6xy + y² = 6

Summary:

dy/dx by implicit differentiation of x² - 6xy + y² = 6 is dy/dx = (x - 3y)/(3x - y)