Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 327: 24

$$ f'(x)= -4e^{-x}-14e^{-2x}.$$

Recall that $(e^x)'=e^x$ Since we have $$ f(x)=4e^{-x}+7e^{-2x}$$ then the derivative $ f'(x)$, using the chain rule, is given by $$ f'(x)=4e^{-x}(-x)'+7e^{-2x}(-2x)'=-4e^{-x}-14e^{-2x}.$$