If 4x2+3x+xy=2 and y(2)=–10 , find y'(2) by implicit differentiation.

i keep getting the wrong answer for this problem evn when plugging 2 in for y.

you can try this....

so f'(x)= -8x-3/(1+ xy)

Plug in 10 for x and 2 for y

(-8(-10)-3)/(1+(-10)(2)= -3.66667

how do u get the - 8x over one?

To find the derivative of y with respect to x, denoted as y', using implicit differentiation, we need to differentiate both sides of the equation with respect to x. Let's go step by step.

Step 1: Differentiate both sides of the equation with respect to x.
Take the derivative of each term on both sides. The left-hand side of the equation will involve the product rule, as it contains the xy term.

On the left-hand side:
d/dx (4x²) = 8x
d/dx (3x) = 3
d/dx (xy) = x(dy/dx) + y

On the right-hand side, the constant term 2 differentiates to zero.

So we have: 8x + 3 + x(dy/dx) + y = 0

Step 2: Simplify the equation.
Rearrange the equation to isolate the term dy/dx, which represents y'.

x(dy/dx) + y = -8x - 3
x(dy/dx) = -y - 8x - 3

Step 3: Substitute the given value.
Plug in the particular value y(2) = -10 when x = 2.

2(dy/dx) = -(-10) - 8(2) - 3
2(dy/dx) = 10 - 16 - 3
2(dy/dx) = -9
(dy/dx) = -9/2

Therefore, y'(2) (the derivative of y with respect to x when x = 2) is -9/2.

Make sure to double-check your calculations to avoid any arithmetic errors.