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Math Help - Product rule problem - cannot find answer.

  1. #1
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    Product rule problem - cannot find answer.

    Hey guys, this is likely a really simple problem I have here.

    basically my problem is to find the derivative of  \frac {-18}{(x^2 - 9)^2}

    So I make that  (-18)(x^2 - 9)^-2 so I can use the product rule.

    So the derivative of  (x^2 - 9)^ -2) is  \frac {2x}{(x^2 - 9)^2}

    I do not know how to find the derivative of -18. I need this derivative to use the product rule, right? I believe it to be 0 or 1... but I have no idea. Please help!
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  2. #2
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    Hello buddy.

    Quote Originally Posted by Kakariki View Post
    Hey guys, this is likely a really simple problem I have here.

    basically my problem is to find the derivative of  \frac {-18}{(x^2 - 9)^2}

    So I make that  (-18)(x^2 - 9)^-2 so I can use the product rule.
    I would say you find the derivative of (x^2 - 9)^-2 by using the chain rule

    Quote Originally Posted by Kakariki View Post
    So the derivative of  (x^2 - 9)^ -2) is  \frac {2x}{(x^2 - 9)^2}
    It is not!

    let f(x) := (x^2-9)^{-2}

    Using the chain rule leads to

    f'(x) = -2*2x*(x^2-9)^{-2-1} = -4x*(x^2-9)^{-3}

    Quote Originally Posted by Kakariki View Post
    I do not know how to find the derivative of -18. I need this derivative to use the product rule, right? I believe it to be 0 or 1... but I have no idea. Please help!
    The derivative of -18 is "0".

    If you want to find the derivative of  x^1 it is 1* x^{1-1} = 1*x^{0} = 1*1 by definition, so it is equal to one

    -18 has no x in it, so it is a constant -> the derivative of a constant is 0

    And in your example you do not need to use the product rule, because -18 is a factor of (x^2-9)^{-2}.


    So the solution is  -18*[(x^2-9)^{-2}]' = -18 * (-4x*(x^2-9)^{-3})

    You can use the product rule -> but you need to use that [-18]' = 0.

    Any more questions?

    Rapha
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  3. #3
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    That was a rather terrible mistake of mine. I guess I was not thinking when doing the derivative of  (x^2 - 9)^-2 . I thought that the derivative of (-18) would be 0, but it wasn't working out with my answer, and you pointed out why! Thank you very much!
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