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1)How is this letter or symbol pronounced mathematically?

$$\overline k$$

2) $'$ is this sign just a symbol of derivative? For example:

$$k'$$ Do we only understand this as a derivative?

Student
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  • "$k$ bar", or "bar $k$" for the first. For the second, the answer is "no", because the "prime" symbol sometimes is just a way to mark a variable making it into a new variable, similar to the way numerical subscripts are used. So $k$, $k'$, $k''$, $k_1$, $k_2$ are sometimes all regarded as just different variables. – Lee Mosher Sep 26 '17 at 11:48
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    "k bar" and "k dash". They can mean whatever you want them to mean and whatever you tell the reader they mean. – Paul Sep 26 '17 at 11:49
  • $\bar{k}$ can be pronounced as $k$ bar. In statistics $\bar{k}$ means arithmetic mean. If $k \in \mathbb{C}$, hence $k$ is complex, then $\bar{k}$ sometimes is used for the complex conjugate of $k$. There might also be other usages just to reuse $k$ but to prevent confusion you could write $\bar{k}$. This is most often used when there is some relationship between $k$ and $\bar{k}$. But I have never seen it for denoting derivatives. – MrYouMath Sep 26 '17 at 11:49
  • Usually context will yield whether or not the prime refers to Newton's prime derivative notation or just simply to new variable. For instance, in an ODE class you'll see e.g. $y''+cy=0$. But in another class you might see e.g. "let $n,n' \in \mathbb{Z}$, such that $n\neq n'$... ." – Nap D. Lover Sep 26 '17 at 11:52
  • k bar 2) sometimes primes are used for other things, for example $k'$ could just be a variable name.
    • – littleO Sep 26 '17 at 11:53
  • I am very grateful for this wonderful information. to all of you. – Student Sep 26 '17 at 11:56
  • @kimchilover I disagree. I did not receive my early mathematical training in Britain or America. I mean $k'$ when I say '$k$ prime'. The place where I receive my early mathematical training has stronger historical connection with Britain than wih America. –  Sep 26 '17 at 12:13