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# Why are the brackets 'dropped' on the denominator of the second derivative ? watch

1. Hi, just wondering why it's dropped?
I attached a pic from the textbook for what I mean.. is it just a standard convention?

Also, how does d^2y/dx^2 work? I understand the rule with it being >0 is minimum and <0 maximum but what is the logic behind that? The textbook didn't really explain it great...

Thanks!
2. Second derivative can be written as d^2y/dx^2 or f '(x) or y'(x). It's just a way of writing it which is ok as long as it is understood that it means the second derivative - which it is.
3. (Original post by B_9710)
Second derivative can be written as d^2y/dx^2 or f '(x) or y'(x). It's just a way of writing it which is ok as long as it is understood that it means the second derivative - which it is.
Sorry I meant why is it not written as d^2y/(dx)^2 like the book illustrates? Is it because you can't 'square' the delta?

Sean any idea?
4. (Original post by Jitesh)
Sorry I meant why is it not written as d^2y/(dx)^2 like the book illustrates? Is it because you can't 'square' the delta?

Sean any idea?
I'm not sure, as far as I know that's just convention/how it's written.

Think of it as the rate of change of the gradient. If you sketch the graph of y = x^2 and look at the points around (0,0) which we already know to be a minimum.

The first derivative is 2x and the second is 2. So when x is less than 0 (to the left of x=0) the gradient is negative and when x is greater than 0 it is positive, so the rate of change of the gradient makes the gradient go from negative to positive, so the rate of change of the gradent is >0 when the point is a minimum.
5. (Original post by SeanFM)
I'm not sure, as far as I know that's just convention/how it's written.

Think of it as the rate of change of the gradient. If you sketch the graph of y = x^2 and look at the points around (0,0) which we already know to be a minimum.

The first derivative is 2x and the second is 2. So when x is less than 0 (to the left of x=0) the gradient is negative and when x is greater than 0 it is positive, so the rate of change of the gradient makes the gradient go from negative to positive, so the rate of change of the gradent is >0 when the point is a minimum.
Thanks Sean! Seems like no one knows why so I guess it's going to be something I will just have to accept!

Would give rep but I've given it too early beforehand and it's not letting me lol
6. (Original post by Jitesh)
Sorry I meant why is it not written as d^2y/(dx)^2 like the book illustrates? Is it because you can't 'square' the delta?

Sean any idea?
It's just notation. Leibniz decided to write it like that.

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