Second order derivative

[Pavi. vr]

The second last line...please help me understand it, why's there a y double dash all of a sudden?

 

[Dr.Peterson]

The second last line...please help me understand it, why's there a y double dash all of a sudden

Here is a more readable image:



What you call "y double dash" is read "y double prime", and is the second derivative. It appears that derivatives are for some reason denoted as subscripts in the problem statement. Is that something you were taught?

They took the derivative twice, the second time as an implicit derivative after multiplying.

 

[Pavi. vr]

Here is a more readable image:

View attachment 37306

What you call "y double dash" is read "y double prime", and is the second derivative. It appears that derivatives are for some reason denoted as subscripts in the problem statement. Is that something you were taught?

They took the derivative twice, the second time as an implicit derivative after multiplying.

We were thaught to read it as 'y double dash', and not write it in the dy/dx form as the problem would look cluttered. While solving it my brain had completely forgotten that the product rule existed and that they just took the derivative twice as you said, looking at it now it's such a simple problem! Thank you for taking the time to answer!

 

[Dr.Peterson]

We were taught to read it as 'y double dash'

Interesting. Clearly you are in a different culture than mine; dialects vary a lot. To me, a dash is "-", and " ' ", in this context, is "prime".

I'm always interested when I see different usages; this is one I wouldn't see often because people don't usually write out how they read symbols! Now I find with a quick search that, indeed, "dash" seems to be standard in Britain and other places. (So why doesn't Wikipedia seem to mention this?)

You learn something new every day!