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# Why do you say 'd two y over dx squared'? watch

1. Why is it 'd two' and not 'd squared'? I've always been told to note that it's 'd two' but I've never been told why.
2. (Original post by gcsemusicsucks)
Why is it 'd two' and not 'd squared'? I've always been told to note that it's 'd two' but I've never been told why.
I've always said d squared y over d x squared. That's what my maths teachers always said.
3. Because it's the second derivative. d isn't an algebraic term, you can't square it.
4. (Original post by gcsemusicsucks)
Why is it 'd two' and not 'd squared'? I've always been told to note that it's 'd two' but I've never been told why.
This is easier to understand if, instead of dy/dx, you write d/dx (y). The d/dx is an isntruction - "I am going to differentiate with respect to x", so d/dx (y) means "I am going to differentiate y with respect to x".

Now suppose you are going to do this twice, one after the other. This is d/dx (d/dx (y)). Leaving the y our of it, the instruction becomes d2 / (dx)(dx), and it makes sense to write this as d2/(dx)^2. So this means "I am going to differentiate twice with respect to x", and we say the "two" to emphasise this. If anything, it is the "dx squared" part which is a slight abuse of the concept, but that's the convention...
5. (Original post by Pangol)
This is easier to understand if, instead of dy/dx, you write d/dx (y). The d/dx is an isntruction - "I am going to differentiate with respect to x", so d/dx (y) means "I am going to differentiate y with respect to x".

Now suppose you are going to do this twice, one after the other. This is d/dx (d/dx (y)). Leaving the y our of it, the instruction becomes d2 / (dx)(dx), and it makes sense to write this as d2/(dx)^2. So this means "I am going to differentiate twice with respect to x", and we say the "two" to emphasise this. If anything, it is the "dx squared" part which is a slight abuse of the concept, but that's the convention...
Thanks so much for the easy to understand explanation! Great to finally know why this is!

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