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What is the derivative of (3x)/(2x^2-18)

Guest Nov 27, 2018
 #1
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"What is the derivative of (3x)/(2x^2-18)?"

 

Let u = 3x and v = (2x2-18)-1

 

Use the chain rule:  duv/dx = udv/dx + vdu/dx:

 

du/dx = 3      dvdx = -(2x2-18)-24x

 

d(3x(2x2-18)-1)/dx = -12x2(2x2-18)-2 + 3(2x2-18)-1 

 

or  (3(2x2-18) - 12x2)/(2x2-18)2   →  -(6x2 + 54)/(2x2-18)2 → -(3/2)(x2 + 9)/(x2 - 9)2

Alan  Nov 27, 2018
 #2
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Thanks for the response! I used the quotient rule and got the answer (-6x^2-54)/(2x^2-18)^2

I'm not sure where I'm going wrong. 

Guest Nov 27, 2018
 #3
avatar+14556 
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That IS the same answer Alan posted!   Good work....cheeky

ElectricPavlov  Nov 27, 2018
 #4
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He simplified it further by factoring right? Do I not need to do that? 

Guest Nov 27, 2018
 #5
avatar+14556 
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I do not believe you need to factor it to be correct.    You found the derivative as asked.

ElectricPavlov  Nov 27, 2018

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