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October 29th, 2009, 05:22 PM   #1
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should i apply the product rule or quotient rule?

alright, so im attempting this question here...and i've tried it both ways..but am not ending up with the same answer, so am i way off ?

find the derivitave of y = 2x^3/(4x-1)^4

(2x^3)(4x-1)^-4

(6x^2)(4x-1)^-4 +( 2x^3)(4)

or

2x^3(4x-1)^-4

(4)-8x^3(4x-1)^-5

or

a combination of quotient rule and the general power rule
(6x^2)(4x-1)^4(4)(4x-1)^3 - (2x^3)(4)(2x^3)

ugh i think im lost, any tips would be great, thanks!
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October 29th, 2009, 06:03 PM   #2
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Re: should i apply the product rule or quotient rule?

The product rule and quotient rule should yield the same answer under ANY circumstances.

Using product rule, we have


Simplying it further will give you the answer


Using quotient rule, we have



Simplying it further will give you the same answer

Cheers
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October 29th, 2009, 06:24 PM   #3
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Re: should i apply the product rule or quotient rule?

just a question tho... during the product rule when you listed

6x^2(4x-1)^-4 - 8x^3(4x-1)^-5 ( dont you need to multiply this by the derivitave of (4x-1)^-4..which would be 4? i know you multipied this by 4 already..because of the general power rule..but i thought you had to also multiply it by the derivitave of (4x-1)^-4 when using that power rule. hope that wasnt too confusing, thanks!

only reason im following that " rule is because if y = (3x-4)^6 and the derivitave ofthat is 6(3x-4)^5(3) = 18(3x-4)^5 ...and i see you didnt use that chain rule in that question, i know im wrong, im jsut curious what you did.
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October 29th, 2009, 11:58 PM   #4
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Re: should i apply the product rule or quotient rule?

yea.. you are right
i just made the correction.
That's one of dumbest mistake i have ever made
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