Chapter 3 - Section 3.2 - The Product and Quotient Rules - 3.2 Exercises - Page 189: 6

$y'=\dfrac{e^{x}}{(1-e^{x})^{2}}$

$y=\dfrac{e^{x}}{1-e^{x}}$ Differentiate using the quotient rule $y'=\dfrac{(1-e^{x})(e^{x})'-(e^{x})(1-e^{x})'}{(1-e^{x})^{2}}=\dfrac{(1-e^{x})(e^{x})-(e^{x})(-e^{x})}{(1-e^{x})^{2}}=...$ Evaluate the products in the numerator $...=\dfrac{e^{x}-e^{2x}+e^{2x}}{(1-e^{x})^{2}}=\dfrac{e^{x}}{(1-e^{x})^{2}}$ $y'=\dfrac{e^{x}}{(1-e^{x})^{2}}$