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Math Help - Derivative Questions?

  1. #1
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    Derivative Questions?

    How do I solve these problems?????--to find the derivative
    1. y=(x+1)^2(x^2+2x)

    2. y=x/x+1
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  2. #2
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    Hi there montenegro3, welcome to MHF!

    Quote Originally Posted by montenegro3 View Post
    How do I solve these problems?????--to find the derivative
    1. y=(x+1)^2(x^2+2x)

    To differentiate this function you must employ the product rule.

    It states that if

    y = u\times v \Rightarrow y' = vu'+uv'

    in your case make u = (x+1)^2 and v = x^2+2x

    find u' and v' and apply the rule


    Quote Originally Posted by montenegro3 View Post

    2. y=x/x+1
    Use the quotient rule here, it states if

    For y = \frac{u}{v} \Rightarrow y' = \frac{vu'-uv'}{v^2}

    in your case make u = x and v=x+1

    find u' and v' and apply the rule
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  3. #3
    MHF Contributor matheagle's Avatar
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    Instead of the quotient rule, you should rewrite that ratio as...

     {x\over x+1}={(x+1)-1\over x+1}= 1- {1\over x+1}= 1- (x+1)^{-1}

    Hence the derivative is   (x+1)^{-2}
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