Derivatives in Halliday's physics book?

In summary, the conversation discusses the differentiation of a function and the resulting equations. The first equation, d(72t²)/dt = 144t, is a basic example of differentiation and the result of 144 is due to the constant 72 being multiplied by the power of t, which is 2. The second equation, 4t²+2t+3 = 8t+2, is also a basic differentiation problem and the result is due to the constant 4 being multiplied by the power of t, which is 2. The conversation also mentions the need to understand calculus in order to fully understand these concepts.
  • #1
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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  • #2
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 ?
 
  • #3
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.
 
  • #4
But this is not integration, it is differentiation !
 
  • #5
This physics text is calculus based. You will need to learn calculus before attacking that text, I'm afraid.
 
  • #6
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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  • #7
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?
 

What are derivatives in physics?

Derivatives in physics refer to the rate of change of a physical quantity with respect to another quantity. They are used to describe how a physical quantity changes over time or space.

Why are derivatives important in Halliday's physics book?

Derivatives play a crucial role in Halliday's physics book as they are used to describe the motion and behavior of physical systems. They are particularly important in understanding concepts such as velocity, acceleration, and force.

How are derivatives used in solving physics problems?

Derivatives are used in physics problems to find the instantaneous rate of change of a physical quantity, which can then be used to calculate other important quantities such as velocity and acceleration. They are also used to find the slope of a curve and determine the direction of motion.

What are the different types of derivatives used in Halliday's physics book?

Halliday's physics book uses several types of derivatives, including the derivative of a constant, the derivative of a power function, the derivative of an exponential function, and the derivative of a trigonometric function.

Are derivatives only used in mechanics in Halliday's physics book?

No, derivatives are used in various branches of physics covered in Halliday's book, including mechanics, thermodynamics, electromagnetism, and quantum mechanics. They are a fundamental tool for describing the behavior of physical systems in these areas.

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