How do I find the derivative of d(x(t)2)/dt?

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Homework Help Overview

The discussion revolves around finding the derivative of the expression d(x(t)²)/dt, focusing on the application of differentiation rules in calculus.

Discussion Character

  • Mathematical reasoning

Approaches and Questions Raised

  • Participants explore the use of the chain rule and substitution in differentiating the expression. There is a discussion about justifying the steps taken in the differentiation process.

Discussion Status

Some participants confirm the correctness of the approaches discussed, while others suggest alternative methods for clarity. The conversation indicates a productive exchange of ideas regarding the differentiation process.

Contextual Notes

There is an emphasis on understanding the chain rule and its application, with some participants questioning the necessity of substitution in the differentiation process.

tomwilliam
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Homework Statement


d(x(t)2)/dt


Homework Equations





The Attempt at a Solution



I guess that this should be:

2x(dx/dt)
but I'm not sure how to justify it:
u= x
d(u2)/du = 2u

(d(u2)/du)(du/dt) = d(u2)/dt

So 2u(du/dt) = 2x(dx/dt)
Is this right?
 
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Yes, that's just the chain rule.
 
hi tomwilliam! :smile:

you don't need to use substitution …

just say d(x(t)2)/dt = d(x(t)2)/d(x(t)) d(x(t))/dt = 2x dx/dt :wink:
 
Oh yes. Thanks for that.
 

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