Hi guys, I haven't posted in a while but I was tutoring someone and ran into a problem that I thought had got right but blackboard said was incorrect.

The problem is

Now find the second derivative when x = 2 and y =1

I keep getting 3/4 as my answer. I solved it using implicit differentiation and also using partials differentiation to double check. The correct answer according to blackboard is -14/27

and can someone show me what im doing wrong with my latex. Guess im a bit rusty. Thanks