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

1. Jun 15, 2010

### theBTMANIAC

1. The problem statement, all variables and given/known data Find the first derivative of [...] (below)

2. Relevant equations

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

3. The attempt at a solution

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

$$y' = \frac{(x^2)(2x+5-0)-((x^2)+5x+-1)(2x)}{x^4} \\ y' = \frac{2x^3+5x^2-2x^3-10x^2+2x}{x^4} \\ y' = \frac{(-5x^2)+2x}{x^4} \\ y' = \frac{-5x+2}{x^3}$$

Is this correct? It feels "off."

Last edited: Jun 15, 2010
2. Jun 15, 2010

### matt_crouch

thats what i got.... =]

3. Jun 15, 2010

### theBTMANIAC

Cool. Thank you. :)

4. Jun 15, 2010

### HallsofIvy

Staff Emeritus
However, the simplest way to do that is write
$$\frac{x^2+ 5x- 1}{x^2}= \frac{x^2}{x^2}+ \frac{5x}{x^2}- \frac{1}{x^2}= 1+ 5x^{-1}- x^{-2}$$

The derivative of that is, of course, $-5x^{-2}+ 2x^{-3}$.

Can you see that that is equal to your result?

5. Jun 15, 2010

### Anonymous217

You can also apply the product rule if HallsofIvy's method doesn't work out (for example, if the denominator is more complicated).