So if we are differentiating the y-side of the function, it goes something like this: Let the function be tan(y)=x

I'm having problems understand why it is done like this and it is not touched upon in my lectures. It just seems to be taken for granted.

Why do we differentiate the y-side and then multiply it by y' ? And whatISy' ?! Shouldn't it be the same thing as d/dy of the y-side?

Hope I'm not too confusing!

Thanks!