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Math Help - Product rule

  1. #1
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    Product rule

    Starting with x^(1/2) * e^x

    i have gotten to g`(x) = x^(1/2)(e^x) + e^x(1/2x^(-1/2))

    what would be the next algebraic (sp) step?
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  2. #2
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    factor out e^x, perhaps also factor out x^(-1/2)
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  3. #3
    Senior Member mollymcf2009's Avatar
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    Quote Originally Posted by TastyBeverage View Post
    Starting with x^(1/2) * e^x

    i have gotten to g`(x) = x^(1/2)(e^x) + e^x(1/2x^(-1/2))

    what would be the next algebraic (sp) step?

    You could also move the x^{-\frac{1}{2}} to the denominator as \sqrt x

    \frac{e^x}{2\sqrt x} + e^x\sqrt x

    I guess if you wanted to do more, you could get a common denominator and combine the two. Not sure how far your teacher wants you to take it.
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