Ok, I know the answer is probably no, and I feel stupid asking it, but say we have an equation (I can't say function for reasons that will become obvious), lets say
Now lets say I differentiate it implicitly and solve for y'. that is the derivative at a point.
Now bear with me if this is really bad but could we do this
Then will differentiating implicitly give the same answer as...
Maybe I am just really lucky, but after pondering this and thinking about it analytically I tried a couple of problems and it seems to pan out, but I do not think it is true, otherwise my book would have it or I would have heard of it.
Can someone please clarify?
The more I think about it, the more I don't think so.
The reason is the difference in the chain rule
But I am pretty sure
Is that right?
I have done some more thinking and a little experimentation and I think that I was right
but I think that it is actually