The equation defines implicitly as a function of and . Find at the point
The solution was as follows:
So if we derive with respect to we get
Plugging inn we get .
But when we differentiate with respect to , on the last expression they used the chain rule on and and treated as a constant. Shouldn't you also use the chain rule on and get something like .
I realize now that since in our point, the last expression would actually fall away and we would get the right answer. But the solution doesn't contain the last expression at all, so I'm confused about whether or not I've misunderstood implicit differentiation.