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Differentiation$\displaystyle y=\frac{(2+e^{-x})^2}{e^x}$ How to differentiate? |

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

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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