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

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

Guest Nov 27, 2018

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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

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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

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That IS the same answer Alan posted! Good work....

ElectricPavlov Nov 27, 2018

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He simplified it further by factoring right? Do I not need to do that?

Guest Nov 27, 2018

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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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