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Math Help - Derivatives - product/quotient/chain rule

  1. #1
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    Derivatives - product/quotient/chain rule

    It would be greatly appreciated if anyone can provide a detailed solution to finding the derivative of; (x^2 - 9) sqrt(x+2)

    Thanks in advance!
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    Quote Originally Posted by Archduke01 View Post
    It would be greatly appreciated if anyone can provide a detailed solution to finding the derivative of; (x^2 - 9) sqrt(x+2)

    Thanks in advance!
    use the product rule ... let's see what you get.
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    I keep getting [2x(x+2) + (x^2 + 9)] / sqrt (t+2).

    I need someone to provide steps so I can see where I went wrong.
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    product rule ...

    \frac{d}{dx}(f \cdot g) = fg' + gf'


    \frac{d}{dx}[(x^2-9)\sqrt{x+2}]

    (x^2-9) \cdot \frac{1}{2\sqrt{x+2}} + \sqrt{x+2} \cdot 2x
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    Thanks, I know the product rule - my answer was the simplified version of what that but somewhere in my simplification I went wrong. How do I proceed from what you've posted? Or is that as far as we're supposed to go?
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    Quote Originally Posted by Archduke01 View Post
    Thanks, I know the product rule - my answer was the simplified version of what that but somewhere in my simplification I went wrong. How do I proceed from what you've posted? Or is that as far as we're supposed to go?
    common denominator is 2\sqrt{x+2} ... proceed from there.

    you should get \frac{5x^2 +8x - 9}{2\sqrt{x+2}}
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