Take the derivative respect to U

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Homework Help Overview

The discussion revolves around taking the derivative of the equation V = √(T/u) with respect to u, where T is treated as a constant. Participants are exploring the differentiation process and the implications of constant factors in the equation.

Discussion Character

  • Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss rewriting the equation in a different form to facilitate differentiation, questioning the treatment of constants and the application of derivative rules. There is an exploration of the correct form of the derivative and the inclusion of constants in the final expression.

Discussion Status

Several participants have provided feedback on the differentiation attempts, with some affirming the correctness of the original poster's approach. There is an ongoing exploration of the correct representation of the derivative, and while some guidance has been offered, no explicit consensus has been reached.

Contextual Notes

Participants are navigating the rules of differentiation while considering the implications of treating T as a constant. There is a mention of a generic formula for differentiation, indicating a potential gap in understanding that is being addressed through discussion.

afcwestwarrior
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V = \sqrt{T/u}

Take the derivative respect to U. I'm having trouble with this.

\sqrt{T} * 1/\sqrt{u}


So would u look like this U^-(1/2)

since T is constant I'd leave it alone.

it would become -(1/2) * u^(-3/2)


Am I right or Am I wrong.
 
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Right now you can re-write the equation as V= T^(1/2)*u^(-1/2)
effectively this is in the form of y=c*x^n (just to go back to familiar notation)
what is the generic formula for this? Your close, but your leaving out the constant...

So what would the answer be once you include it?
 


V= T^(1/2)*-(1/2) * u^(-3/2)
 


looks pretty good to me!
 


since T is a constant your answer is right
 


Thanks for the assistance!
 

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