Derivative of (x^2+5x-1)/(x^2)

  • #1

Homework Statement

Find the first derivative of [...] (below)



Homework Equations



((x^2)+5x-1)/(x^2)

The Attempt at a Solution



(x^2+5x-1)/(x^2)

[tex]y' = \frac{(x^2)(2x+5-0)-((x^2)+5x+-1)(2x)}{x^4}

\\
y' = \frac{2x^3+5x^2-2x^3-10x^2+2x}{x^4}

\\ y' = \frac{(-5x^2)+2x}{x^4}

\\ y' = \frac{-5x+2}{x^3}

[/tex]

Is this correct? It feels "off."
 
Last edited:

Answers and Replies

  • #2
161
1
thats what i got.... =]
 
  • #3
Cool. Thank you. :)
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,847
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However, the simplest way to do that is write
[tex]\frac{x^2+ 5x- 1}{x^2}= \frac{x^2}{x^2}+ \frac{5x}{x^2}- \frac{1}{x^2}= 1+ 5x^{-1}- x^{-2}[/tex]

The derivative of that is, of course, [itex]-5x^{-2}+ 2x^{-3}[/itex].

Can you see that that is equal to your result?
 
  • #5
354
2
You can also apply the product rule if HallsofIvy's method doesn't work out (for example, if the denominator is more complicated).
 

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