First Derivative of (5/x)+(5/SQRT(x)): Homework Equations & Rules to Solve

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Homework Help Overview

The discussion revolves around finding the first derivative of the expression (5/x) + (5/SQRT(x)), which falls under the subject area of calculus, specifically differentiation.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of different derivative rules, including the quotient rule and power rule, while questioning the necessity of each approach. There is an attempt to clarify the application of these rules in the context of the given expression.

Discussion Status

The conversation includes some guidance on how to approach the differentiation, with participants exploring various methods without reaching a definitive consensus on the preferred technique.

Contextual Notes

There is an implicit consideration of whether the problem requires specific rules for differentiation, as well as the potential for simplification in the approach taken.

Government$
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Homework Statement


Find the first derivative of (5/x)+(5/SQRT(x))


Homework Equations



Derivative ruls

The Attempt at a Solution


attachment.php?attachmentid=53629&stc=1&d=1354648651.jpg


Is this correct? Thank you
 

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Yes.
 
Thank you
 
Unless this problem requires the use of the quotient rule, it can be done much more simply using the power rule.

$$\frac{d}{dx}\left(\frac{5}{x} + \frac{5}{\sqrt{x}} \right)$$
= d/dx(5x-1 + 5x-1/2)
= -5x-2 - (1/2)x-3/2
 

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