A particle moves along the x-axis with velocity dx/dt=f(x)

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Discussion Overview

The discussion revolves around the application of the chain rule in calculus to determine the acceleration of a particle moving along the x-axis, where the velocity is defined as dx/dt = f(x). Participants are exploring how to differentiate the velocity function to find the acceleration, which is suggested to be f(x) * f '(x).

Discussion Character

  • Homework-related
  • Mathematical reasoning

Main Points Raised

  • Some participants express uncertainty about using the chain rule and seek clarification on its application.
  • There is a suggestion that the acceleration can be expressed as f(x) * f '(x), but this is not universally accepted or confirmed.
  • One participant prompts others to think about how to differentiate f(x) with respect to time.

Areas of Agreement / Disagreement

The discussion remains unresolved, with participants expressing uncertainty and seeking guidance on the application of the chain rule without reaching a consensus on the acceleration expression.

Contextual Notes

Participants have not fully articulated the assumptions or definitions necessary for applying the chain rule in this context, and there are unresolved steps in the differentiation process.

hyper
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I think I am supposed to use the chain rule in this exercise, but I don't know how to. Please helt me.

A particle moves along the x-axis with velocity dx/dt=f(x). Show that the particle's acceleration is f(x)*f '(x).
 
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hyper said:
I think I am supposed to use the chain rule in this exercise, but I don't know how to. Please helt me.

A particle moves along the x-axis with velocity dx/dt=f(x). Show that the particle's acceleration is f(x)*f '(x).
Can you start by writing down the chain rule?
 


Hootenanny said:
Can you start by writing down the chain rule?

dy/dt= dy/du * du/dt
 


Well next, think of how to apply it. Think of how to differentiate f(x) with respect to time.
 

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