Chapter 3 - Section 3.2 - The Product and Quotient Rules - 3.2 Exercises - Page 189: 9

$y'=\dfrac{1-x}{e^{x}}$

$y=\dfrac{x}{e^{x}}$ Differentiate using the quotient rule: $y'=\dfrac{(e^{x})(x)'-(x)(e^{x})'}{(e^{x})^{2}}=\dfrac{e^{x}-xe^{x}}{e^{2x}}$ Take out common factor $e^{x}$ $y'=\dfrac{e^{x}(1-x)}{e^{2x}}=\dfrac{1-x}{e^{x}}$ $y'=\dfrac{1-x}{e^{x}}$