If 3x²+ 2xy + y²= 2, then the value of dy/dx at x = 1 is?

Implicit differentiation means differentiating or finding the derivative with respect to one of the variables and keeping others as constants.

Answer: The differentiation of the expression 3x²+ 2xy + y²= 2 at x = 1 is not defined.

Let us proceed step by step

Explanation:

Given Expression: 3x²+ 2xy + y²= 2

When x = 1 then y = -1 [ by substituting the value of x in the above expression ]

Differentiating on both the sides of the given expression with respect to x, we get:

(d / dx) (3x²+ 2xy + y²) = (d / dx) (2)

⇒ 6x + 2 [x dy / dx + y] + 2y dy / dx = 0 [ d / dx (xy) = x dy/dx + y using product rule of differentiation ]

⇒ 6x + 2x dy / dx +2y dy / dx + 2y = 0

⇒ [2x + 2y] dy / dx + 6x + 2y = 0

⇒ dy / dx = -6x + 2y / [2x + 2y]

On substituting the value of x = 1 and y = -1, we get

⇒ dy / dx = not defined [ anything divided by 0 is not defined ]