Use "implicit differentiation" which is basically using the chain rule. Differentiate both sides of the equation with respect to x: [tex](x^2y+ xy^2)'= (x^2y)'+ (xy^2)'. Use the product rule on . Similarly, (that last term is the chain rule). Of course, the derivative of any constant is 0 so the derivative on the right is (6)'= 0. Putting those together,
. You can x= 1, y= 3 to get an equation to solve for y' at that point.
Now go ahead and use the product and chain rules to differentiate again.
. Put x= 1, y= 3, and y' equal to whatever you got above and solve the equation for y''.