Chapter 3 - Section 3.2 - The Product and Quotient Rules - 3.2 Exercises - Page 188: 12

$f'(z)=-ze^{z}-2e^{2z}+1$

$f(z)=(1-e^{z})(z+e^{z})$ Differentiate using the product rule $f'(z)=(1-e^{z})(z+e^{z})'+(z+e^{z})(1-e^{z})'=...$ $...=(1-e^{z})(1+e^{z})+(z+e^{z})(-e^{z})=...$ Evaluate the products and simplify $...=1-e^{2z}-ze^{z}-e^{2z}=-ze^{z}-2e^{2z}+1$