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Math Help - Quotient Rule maybe?

  1. #1
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    Quotient Rule maybe?

    So, I am stuck on a problem.

    If I need to get the derivative of e^(x)/(x+1), would I use the quotient rule on the ^(x)/(x+1)? I am not certain what to do with the fraction power. Thanks for any help.
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  2. #2
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    Reply

    y = e^{\frac{x}{x+1}}

    differentiate, use chain rule,

    y'=  e^{\frac{x}{x+1}}. \frac{d}{dx}\left(\frac{x}{x+1}\right)

    Now apply Quotient rule to fraction part.

    y'=  e^{\frac{x}{x+1}}\left(\frac{1.(x+1)-x.1}{(x+1)^2}\right)

    y'=  e^{\frac{x}{x+1}}\left(\frac{1}{(x+1)^2}\right)

    y'=  \frac{1}{(x+1)^2}.e^{\frac{x}{x+1}}
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