Implicit Differentiation - example question

I was doing so well until I wrote the fraction in the last line upside down (numerator should be the denominator, and vice versa).

[jacobhouston]

I love how this dude takes his time to explain the long way and the reason why he teaches us tools.
Mediocre professors rush to the solution, he doesn’t. Which makes the information memorable.

[drfpslegend]

Good explanation, but the final answer is wrong. The top and the bottom should be switched.

[cartmanthesecond]

Over the last few weeks you've become my favorite youtuber, as the way you explore topics in your classroom is so inspiring. I love to sit down and try problems like these myself before seeing how you tackle them (your solution was much more succinct than mine, because I had forgotten the derivative of secant and how chain rule works with implicit differentiation). I find it really unfortunate that your videos don't have a larger reach, since I feel they have the power to change how people perceive and approach mathematics.

[krishveerainnovationsandmo]

Shouldn't the denominator and numerator be switched? I mean I get that you took out the negative sign so that you could get the 'y' to be positive, but then how did that make the entire RHS reciprocate?

[apotheosisaurel]

Professor Woo has an amazing talent for teaching. PS: If you are confused about the final step, check the description. (The numerator and denominator should be switched.)

[outcast]

I love mathematics, it is the only science that doesn't lie.

[ronkoren]

funny how the only time he gets a standing ovation is when he writes the wrong solution :P

[missghani]

Mr Woo looks a bit disturbed in this video, but still explained well

[vaiebhavpatil]

Sir you accidentally flipped the answer
Reason for that applause maybe?

[enkephalin]

You have perfectly illustrated why, even though I can understand the principles of the differential operator and implicit differentiation, I get every solution wrong!

[BigmanHaus]

What I'm liking so far about implicit differentiation is that you can leave the most horrible looking answers and get away with it.

[jacksonzheng]

why did you use the product rule when differentiating "xy" on the left-hand side of the equation instead of using the power rule? I thought "xy" were just two variables?