Find derivative of function with fractional exponent?

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Discussion Overview

The discussion revolves around finding the derivative of the function R(t) = 5t^(-3/5). Participants explore the application of derivative rules, particularly in the context of fractional exponents.

Discussion Character

  • Homework-related, Mathematical reasoning

Main Points Raised

  • One participant asks about the derivative rules applicable to the function R(t) = 5t^(-3/5).
  • Another participant confirms that standard derivative rules apply, specifically mentioning that the derivative of x^n is nx^(n-1) for any real number n.
  • A participant proposes that the derivative is -3t^(-1.6), indicating a potential misunderstanding of the exponent notation.
  • A later reply clarifies the derivative calculation, presenting it as -3t^(-8/5) and emphasizing the importance of using fractional notation for clarity.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the preferred notation for the exponent, as one participant suggests decimal notation while another advocates for fractional notation. The calculation of the derivative itself is confirmed, but the notation remains a point of discussion.

Contextual Notes

The discussion includes varying interpretations of exponent notation and its impact on derivative representation. There is also a lack of clarity regarding the initial misunderstanding of the exponent's decimal form.

coolbeans33
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I need to find the derivative of R(t)=5t-3/5

are there any derivative rules I can use for this problem?
 
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Re: find derivative of function with fractional exponent?

Welcome to MHB, coolbeans33! :)

coolbeans33 said:
I need to find the derivative of R(t)=5t-3/5

are there any derivative rules I can use for this problem?

Just the regular ones should do.
I presume you know that the derivative of $x^n$ is $nx^{n-1}$?
This is also true if n is a real number.
Or put otherwise: the derivative of $t^\alpha$ is $\alpha t^{\alpha - 1}$ for any real number $\alpha$.
 
Re: find derivative of function with fractional exponent?

so the answer is -3t-1.6?
 
Last edited:
Re: find derivative of function with fractional exponent?

coolbeans33 said:
so the answer is -3t-1.6?

Yes, although I would only use decimal notation if the exponent is given using such notation. In this case I would write:

$$\frac{d}{dt}\left(5t^{-\frac{3}{5}} \right)=5 \left(- \frac{3}{5} \right)t^{-\frac{3}{5}-1}=-3t^{-\frac{8}{5}}$$
 

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