Question

If 3x^2 + 2xy + y^2=2 then the value of dy/dx at x=1 ?

a) 1
b) -1
c) 2
d) -2

Answer 1

To find the value of dy/dx at x=1, differentiate the given equation with respect to x and solve for dy/dx.

Step-by-step explanation:

To find the value of dy/dx at x=1, we need to differentiate the given equation with respect to x. The equation is 3x^2 + 2xy + y^2 = 2. Differentiating both sides of the equation using the chain rule, we get:

6x + 2y(dy/dx) + 2xy' + 2yy' = 0

Plugging in x=1 into the equation and solving for dy/dx, we get:

6 + 2y(dy/dx) + 2y + 2yy' = 0

Substituting the value of y from the given equation, we get:

6 + 2(dy/dx) + 2 + 2(dy/dx) = 0

Combining like terms, we get:

4(dy/dx) = -10

Simplifying, we find that dy/dx = -10/4 = -2. Therefore, the value of dy/dx at x=1 is -2.