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: 3,002 Thanks: 1587 
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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