Chapter 3 - Section 3.6 - The Chain Rule - Exercises - Page 158: 36

$$y'=-4xe^{-2x}$$

$$y=(1+2x)e^{-2x}$$ The derivative of function $y$ is: $$y'=(1+2x)'e^{-2x}+(1+2x)(e^{-2x})'$$ $$y'=2e^{-2x}+(1+2x)e^{-2x}(-2x)'$$ $$y'=2e^{-2x}-2(1+2x)e^{-2x}$$ $$y'=2e^{-2x}(1-1-2x)$$ $$y'=2e^{-2x}(-2x)$$ $$y'=-4xe^{-2x}$$