If x^2+3y^2=8+2xy, then d^2y/dx^2 at (2,2) =

We are given

x² + 3y² = 8 + 2xy

We are asked for

d^2y/dx^2 at (2,2)

Which is the second derivative of the expression in terms of x evaluated at (2,2)

The expression can't be express explicitly in terms of x

Doing implicit differentiation

2x dx + 6y dy = 2y dx + 2 x dy

Solving for dy/dx

dy/dx = (2x - 2y) / (2x - 6y)

Then,

d^2y/dx^2 at (2,2) can now be determined