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Partial Derivatives

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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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.
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 ?
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.
(edited 11 years ago)
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... :s-smilie:
Original post by Ari Ben Canaan
Just checked the mark scheme.... It says that the equality is untrue... :s-smilie:


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.
(edited 11 years ago)
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.

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 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.
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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