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.

Question

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.

mimi_x3 · Answer

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

anonymous · Answer

yes it is.

anonymous · Answer

Messed up in product rule somewhere.

anonymous · Answer

Maybe double-check your exponents.

anonymous · Answer

uhm.

anonymous · Answer

:)

anonymous · Answer

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.'

anonymous · Answer

i know the formula.

anonymous · Answer

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)

anonymous · Answer

now i re-did it and got 2/x

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

ur doing it wrong.

anonymous · Answer

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

anonymous · Answer

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