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anonymous
 one year ago
Complex Derivatives !!
if y = ((6x3)^4)/((3x+4)^(1/3)) what is dy/dx ?
anonymous
 one year ago
Complex Derivatives !! if y = ((6x3)^4)/((3x+4)^(1/3)) what is dy/dx ?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[y = \frac{ (6x3)^4 }{ \sqrt[3]{3x+4} }\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so let me show you what i got and then tell me what iv done wrong

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2did you move the root to the top as 1/3 power, and apply the product rule

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0!!! no i was doing the quotient rule like the fool i am!!! very clever!!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay let me start over

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2either is good, it isnt too much work

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay so this is what iv got so far \[(24(6x3)^3)((3x+4)^{1/3}) + ((6x3)^4)((3x+4)^{4/3})\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0quick question : i cant distribute the 24 into the (6x3) because its cubed right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so i can distribute the 24?

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2test and see if you forget algebra things... 24(6x  3)^3 = the distributed value?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay sorry lost internet connection,

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2maybe do the quotient rule and see if that is easier

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not sure where to go now, do i just bring down the negative exponents?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[(24(6x3)^3 + (6x3)^4)/((3x+4)^{4/3}+(3x+4)^{1/3})\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2that is the derivative, done..

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2i am sure they want it all simplified though i assume

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yep it seems so , it dosent appear to be any of the answer choices

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2you can move the  exponents , but you can not do that, a * b^1 + c*d^1 is not same as (a +c) / (b + d)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2rather it is just (a/b) + (c/d)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0okay don't worry about the simplification it is just tedious work i think iv got it , thank you very much for your help

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2notice the parenthesis value appears in both terms, for both the different parenthesis, maybe try some factoring

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2\[(24(6x3)^3)((3x+4)^{1/3}) + ((6x3)^4)((3x+4)^{4/3})\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2or, put the negative exponents back to the bottom, then you would have to do the common denominator to add the two fractions

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{ 24(6x3)^3 }{ (3x+4)^{1/3} } + \frac{ (6x3)^4 }{ (3x+4)^{4/3}}\]

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2need to multiply first term by (3x+4)^{3/3} / (3x+4)^{3/3}

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you mean 4/3 for your exponent right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0not that it matters much now but we did it completely wrong, we were suppose to multiply both sides by Ln at the beginning and work from there

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2yes, i just skipped a couple things, the net effect is what i said the common denominator to multiply everything by is the product of the two, so you get (3x+4)^{5/3} that puts the denominator to 5/3 power, and adds a factor of (3x+4)^{1/3} that can factor from the top two terms, so overall you are just multiplying the first fraction by (3x+4)^(3/3)

DanJS
 one year ago
Best ResponseYou've already chosen the best response.2\[\frac{ (3x+4)*24*(6x3)^2 + (6x3)^4 }{ (3x+4)^{4/3} }\]
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