bmelyk 3 years ago Find the derivative of f(x) =2x^2-1/x^2 in three ways : (a) using the quotient rule (b) using the product rule (c) using neither the product rule nor the quotient rule I have already done all of these out. my answers: a) 2/x^3 b)-4x^3+x+8/2 c)2 for each one I've gotten a different answer, just wondering why. I think I'm supposed to get the same answer each time.

1. Mimi_x3

is it:$\frac{2x^2-1}{x^2}$?

2. bmelyk

yes it is.

3. CliffSedge

Messed up in product rule somewhere.

4. CliffSedge

5. Algebraic!

uhm.

6. Algebraic!

:)

7. CliffSedge

For product rule start with f(x) = (2x^2-1)(x^-2) Then it's 'first times the derivative of the second, plus the second times the derivative of the first.'

8. bmelyk

i know the formula.

9. Algebraic!

non-quotient-or-product-rule way would be: 2x^2/x^2 - 1/x^2 =2 -1/x^2 (2 -1/x^2)' = - (-2*x^-3)

10. bmelyk

now i re-did it and got 2/x

11. bmelyk

for the third way i did the definition of the derivative and i only got a 2

12. CliffSedge

You're losing track of an exponent somewhere. What are you getting for the derivative of x^-2 ?

13. bmelyk

i re-did the product rule and got 2/x

14. Algebraic!

ur doing it wrong.

15. bmelyk

okay i got a and b right now, just wondering why my definition of the derivative one is wrong.

16. bmelyk

i got 2/x^3 for a and b but only 2 for the definition of the derivative.