Derivatives in Halliday's physics book?

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SUMMARY

The discussion centers on the differentiation of functions as presented in Halliday's physics book. The derivative of the function f(t) = 72t² is correctly calculated as d(72t²)/dt = 144t, demonstrating the application of basic differentiation rules. Participants emphasize the necessity of understanding calculus fundamentals to grasp these concepts fully. The conversation also highlights the importance of accurately marking the expected response level for clarity in discussions.

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kent davidge
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(sorry my bad english). I was reading a Halliday's book of phyisics awhat I found is below.

d(72t²)/dt = 144t

why did the result was 144? It has anything to do with the deltas in the equation (d and dt)?

and second I don't realize why the result of this another equation is this

4t²+2t+3 = 8t+2

5wgs5d.jpg
 
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These are very simple differentiations. What do you know of differentiating a function ? E.g. the definition of derivative?
The derivative of f(x) = x2 ?
 
well, I know a little bit how to solve an integral by summing all the terms but when I solve it for f(x) = x² I found 72t² and the result is 144t as you can see in the image above.
 
But this is not integration, it is differentiation !
 
This physics text is calculus based. You will need to learn calculus before attacking that text, I'm afraid.
 
I cannot do anything but agree with previous posters. These results are very basic derivatives and you will need to learn calculus properly before you can hope to understand what is going on.

Also, please note that the thread levels are intended for you to mark what level of answer you are comfortable with. The "A" you marked this thread with means that you expect an answer on graduate student level. This is clearly not the case and I have changed the level accordingly.
 
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kent davidge said:
d(72t²)/dt = 144t

why did the result was 144?

What did you think it should have been, and how did you arrive at that result?
 

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