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Math Help - Simple differentiation problem using product rule

  1. #1
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    Simple differentiation problem using product rule

    I'm doing a seemingly simple problem for h.w

    The question is to differentiate (u − squareroot of u)(u+ squareroot of u)

    After applying the product rule I get 2u-1-u^1/2 However when I input it the h.w says it's wrong. can someone please help me?
    Last edited by neontiger94; September 28th 2012 at 08:01 PM.
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Simple differentiation problem using product rule

    I would first rewrite the function as follows:

    f(u)=(u-\sqrt{u})(u+\sqrt{u})=u^2-u

    Now, differentiation is a bit simpler.
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  3. #3
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    Re: Simple differentiation problem using product rule

    but doesn't that disregard the product rule? If i differentiate that I get 2u-1
    Last edited by neontiger94; September 28th 2012 at 08:16 PM.
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  4. #4
    MHF Contributor MarkFL's Avatar
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    Re: Simple differentiation problem using product rule

    It allows you to dispense with the product rule, but you will get the same result either way. It's just simpler in this case to find the product first, then differentiate.
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    Re: Simple differentiation problem using product rule

    Of course, MarkFL2 is correct. The derivative is the same no matter how you find it, so you may as well find it the easiest way. But if you really want to use the product rule, here it is:

    f'(u)=(u-\sqrt{u})(u+\sqrt{u})'+(u-\sqrt{u})'(u+\sqrt{u})
    =(u-\sqrt{u})(1+\frac{1}{2\sqrt{u}})+(1-\frac{1}{2\sqrt{u}})(u+\sqrt{u})
    =(u-\sqrt{u}+\frac{\sqrt{u}}{2}-\frac{1}{2})+(u+\sqrt{u}-\frac{\sqrt{u}}{2}-\frac{1}{2})
    =2u-1

    - Hollywood
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