This question differentiates $y=x$ with respect to $x^2$ by introducing a variable $u$, and answers say his method is valid.
On the other hand, the same technique when used here has been downvoted, and categorized as invalid, whereas the answerer says it is valid. Which one is the case?
I understand the first one is informal, and concerned with the answer. Whereas the other one is concerned with a formal proof.
My question is that if I wish primarily to calculate the derivative (and not prove it), is the introduction of $u$ valid? Also, if I am not interested in differential geometry, and restrict myself to some limited topics, then does the technique become valid?
