## anonymous 4 years ago find the derivative of y=(x²+5-1/x²)² my steps: y'=2[x²+5-x^(-2)](2x+2x) =4x³+20x-4x^(-1) but the answer given is 4x³+20x+20/x³-4/x^5 why am i wrong?

1. Mimi_x3

$y=\left(\frac{x^{2}+5-1}{x^{2}}\right)^{2}$??

2. anonymous

$x^2+5-\frac{1}{x^2}$

3. anonymous

your step was wrong.. at first

4. anonymous

why?

5. lgbasallote

he's right....

6. lgbasallote

well one minor mistake

7. anonymous

what have i done wrong?

8. anonymous

it is derivative of y = (x^2 + 5 - 1)^2 * (x^-2)

9. lgbasallote

the derivative of x^(-2) is not -2x it's -2x^-3

10. lgbasallote

so just change your 2x there with 2x^-3 and you're fine. redo the rest of the solution

11. anonymous

so you use if y = fg y' = f'g + fg'

12. anonymous

lgbasallote, i get it, thanks!

13. lgbasallote

welcome. also...don't forget you still have a 2 outside..you have to distribute it to the equation too

14. anonymous

try use chain rule to solve it

15. anonymous

the eq is not a ratio..

16. anonymous

damn..