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jiasyuen December 28th, 2014 05:19 AM

Differentiation
 
$\displaystyle y=\frac{(2+e^{-x})^2}{e^x}$

How to differentiate?

szz December 28th, 2014 06:12 AM

Use the Chain rule for the numerator and the quotient rule for differentiation.

skeeter December 28th, 2014 06:24 AM

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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