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 October 29th, 2009, 05:22 PM #1 Newbie   Joined: Sep 2009 From: saskatoon Posts: 20 Thanks: 0 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!
 October 29th, 2009, 06:03 PM #2 Member   Joined: Oct 2009 Posts: 52 Thanks: 0 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 $6x^2(4x - 1)^{-4} - 32x^3(4x - 1)^{-5} \\ = \frac{6x^2(4x -1) - 32x^3}{(4x -1)^5} \\$ Simplying it further will give you the answer $\frac{-8x^3 - 6x^2}{(4x-1)^5}$ Using quotient rule, we have $\frac{6x^2(4x-1)^4 - 32x^3(4x - 1)^3}{(4x - 1)^8} \\ = \frac{6x^2(4x -1) - 32x^3}{(4x -1)^5}$ Simplying it further will give you the same answer Cheers
 October 29th, 2009, 06:24 PM #3 Newbie   Joined: Sep 2009 From: saskatoon Posts: 20 Thanks: 0 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.
 October 29th, 2009, 11:58 PM #4 Member   Joined: Oct 2009 Posts: 52 Thanks: 0 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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### use the quotient rule to differentiate y=2x^4-3x/4x-1

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