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January 26, 2021, 11:34:05 pm

Author Topic: Need help understanding this proof  (Read 449 times)  Share 

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Samueliscool223

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Need help understanding this proof
« on: November 29, 2020, 10:32:16 am »
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I was just reading through my maths methods 3 and 4 textbook in advance, and I came across this proof of the product rule that kinda confused me (see attached image below), specifically the 2nd last line. It says as squiggly dx approaches zero, squiggly du/dx becomes normal du/dx, how is this possible? Wouldn't that cause squiggly du/dx to approach du/0 which would be infinity? I don't completely get this, can someone please explain?
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The Cat In The Hat

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Re: Need help understanding this proof
« Reply #1 on: November 29, 2020, 04:18:37 pm »
+1
I was just reading through my maths methods 3 and 4 textbook in advance, and I came across this proof of the product rule that kinda confused me (see attached image below), specifically the 2nd last line. It says as squiggly dx approaches zero, squiggly du/dx becomes normal du/dx, how is this possible? Wouldn't that cause squiggly du/dx to approach du/0 which would be infinity? I don't completely get this, can someone please explain?
This probably isn't the answer you want, but you don't need to understand the proof. You don't need to be able to demonstrate it. (Someone correct me if I'm wrong.) You just need to use the product rule and know how/when to use it, not why it works. I don't even recognise that proof, nor do I recall that there was one. As I see it, it isn't necessary. So make of my answer what you will.
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S_R_K

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Re: Need help understanding this proof
« Reply #2 on: November 29, 2020, 06:57:24 pm »
+4
As TheCatintheHat points out, you are not required to know the proof for the purposes of MM34 exams.

However, to answer your question:

The passage you quote is not intended to be a proof, it is just heuristic argument for why you might expect the product rule to take the form it does. Along these lines, see: https://www.youtube.com/watch?v=YG15m2VwSjA

The standard (and accessible for Year 12 students) proof of the product rule is given in the Cambridge textbook on the previous page, where you write out the difference quotient for f(x)g(x) and then use the standard trick of adding and subtracting f(x+h)g(x) to factorise.
« Last Edit: November 29, 2020, 10:13:31 pm by S_R_K »

Samueliscool223

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Re: Need help understanding this proof
« Reply #3 on: November 30, 2020, 04:18:07 pm »
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This probably isn't the answer you want, but you don't need to understand the proof. You don't need to be able to demonstrate it. (Someone correct me if I'm wrong.) You just need to use the product rule and know how/when to use it, not why it works. I don't even recognise that proof, nor do I recall that there was one. As I see it, it isn't necessary. So make of my answer what you will.
Still it's good to know the proof behind it even if its not relevant to the course in my opinion at least, because it helps you see the logic behind it and better memorise it.
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