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# Partial Derivatives watch

1. So I can do all parts of this question easily except for the last bit.

I've found that the inequality doesn't hold true but I cant come up with a explanation as to why it doesnt.
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2. (Original post by Ari Ben Canaan)
So I can do all parts of this question easily except for the last bit.

I've found that the inequality doesn't hold true but I cant come up with a explanation as to why it doesnt.
You only need an explanation if it does hold true.

Which it does!

PS: It's an equality, not an inequality.
3. (Original post by ghostwalker)
You only need an explanation if it does hold true.

Which it does!

PS: It's an equality, not an inequality.
I did this question yesterday. I have found them to be equal. I think, looking back at my workings, I got answers of 3 in both cases.

Why are they equal ? What is the explanation ?
4. (Original post by Ari Ben Canaan)
I did this question yesterday. I have found them to be equal. I think, looking back at my workings, I got answers of 3 in both cases.

Why are they equal ? What is the explanation ?
Humm! I make it 0.

Edit: Oops, may have misread the question - will check again.
5. (Original post by ghostwalker)
Humm! I make it 0.

Edit: Oops, may have misread the question - will check again.
Just checked the mark scheme.... It says that the equality is untrue...
6. (Original post by Ari Ben Canaan)
Just checked the mark scheme.... It says that the equality is untrue...
Ok, Just rechecked it, and I get G'(x)=3x, and F'(y)=3y.

Unless I made a slip somewhere.

Edit: Yep I made a slip. Doh!

See below.
7. My inputs:

Hope this helps. Peace.
8. (Original post by ghostwalker)
Ok, Just rechecked it, and I get G'(x)=3x, and F'(y)=3y.

Unless I made a slip somewhere.
I'd imagine the easiest way to check that you've made a slip up here is to consider the anti-symmetry of f in x and y.
9. (Original post by Farhan.Hanif93)
I'd imagine the easiest way to check that you've made a slip up here is to consider the anti-symmetry of f in x and y.

(Original post by WhiteGroupMaths)
My inputs:

Hope this helps. Peace.
(Original post by ghostwalker)
Ok, Just rechecked it, and I get G'(x)=3x, and F'(y)=3y.

Unless I made a slip somewhere.

Edit: Yep I made a slip. Doh!

See below.
Seems I made a negative sign vanish in my workings hence the reason why I initially believed the equality was true.

What is the explanation for why they should or should not be equal ? This is just for my own knowledge.
10. You could try pondering over things in the geometrical context.

I wrote this for my advanced math students ages ago, perhaps it might give you some inspiration;

Partial Differentiation 1

Peace.

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