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

## 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)

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

Is this correct? It feels "off."

Last edited:

thats what i got.... =]

Cool. Thank you. :)

HallsofIvy
Homework Helper
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?

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