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
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 ]
Therefore, the differentiation of the expression 3x2+ 2xy + y2 = 2 at x = 1 is not defined.