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