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December 28th, 2014, 05:19 AM   #1
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Differentiation

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

How to differentiate?
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December 28th, 2014, 06:12 AM   #2
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Use the Chain rule for the numerator and the quotient rule for differentiation.
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December 28th, 2014, 06:24 AM   #3
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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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