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 December 28th, 2014, 05:19 AM #1 Senior Member   Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36 Differentiation $\displaystyle y=\frac{(2+e^{-x})^2}{e^x}$ How to differentiate?
 December 28th, 2014, 06:12 AM #2 Senior Member     Joined: Oct 2014 From: EU Posts: 224 Thanks: 26 Math Focus: Calculus Use the Chain rule for the numerator and the quotient rule for differentiation.
 December 28th, 2014, 06:24 AM #3 Math Team     Joined: Jul 2011 From: Texas Posts: 2,975 Thanks: 1571 You may use the quotient rule or rewrite the function as a product & use the product rule. In this case, my preference would be to expand the numerator, divide each term by $\displaystyle e^x$, then take the derivative. $\displaystyle \frac{(2+e^{-x})^2}{e^x}=\frac{4+4e^{-x}+e^{-2x}}{e^x}=4e^{-x}+4e^{-2x}+e^{-3x}$ Take the derivative ... $\displaystyle -4e^{-x}-8e^{-2x}-3e^{-3x}$

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