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Link to the Basic definition's image

What is the theory of the transformation from $f'(x)$ into $\frac{{\partial f}}{{\partial x}}(x,y)$ ? (I don't mean just replace a by y) Could anybody explain shortly and give me some reference? Your help is appreciated.

user2842390
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  • What do you mean by the added sentence "I don't mean just replace $a$ by $y$"? That's what they did -- it's not clear what you mean, if not that. – joriki Aug 24 '16 at 14:48
  • Yeah, at first I understand replacing a by y. I was a little bit confused by symbol. you told me "they substitute y for it again.There isn't more to it than that", giving y into the brackets. It's a basic knowledge. Your answer is clear, I really appreciate. Thanks a lot, Mr Joriki. – user2842390 Aug 24 '16 at 14:54

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They're just replacing $y$ by $a$ to emphasise the fact that $y$ is being considered as a constant in forming the partial derivative with respect to $x$; then, when the derivative has been formed, they substitute $y$ for it again. There isn't more to it than that; if you understand partial derivatives without this detour, there's no need to apply it.

joriki
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