Find dy/dx by implicit differentiation. x² − 4xy + y² = 4

Implicit differentiation is the process of differentiating or finding the derivative of the expression with respect to one of the variables and keeping the rest as constants.

Answer: The value of dy/dx by implicit differentiation of the expression  x² − 4xy + y² = 4 is  (x - 2y) / (2x - y).

Go through the steps to understand the solution better.

Explanation:

Given Expression:  x² − 4xy + y² = 4,

Differentiating on both the sides with respect to x, we get

d/dx ( x² − 4xy + y²) = d/dx (4)

⇒ 2x - 4y - 4x dy/dx + 2y dy/dx = 0 

⇒ 2x - 4y = 4x dy/dx - 2y dy/dx

⇒ 2x - 4y = dy/dx (4x - 2y)

⇒ (2x - 4y) / (4x - 2y) = dy/dx

⇒ (x - 2y) / (2x - y) = dy/dx

Therefore, the value of dy/dx by implicit differentiation of the expression  x² − 4xy + y² = 4 is  (x - 2y) / (2x - y).