Chapter 4 - Applications of the Derivative - 4.9 Antiderivatives - 4.9 Exercises - Page 327: 6

$$ - {e^{ - x}} + C$$

$$\eqalign{ & {\text{The derivative of }}{e^{ - x}}{\text{ is }}\frac{d}{{dx}}\left[ {{e^{ - x}}} \right] = - {e^{ - x}},{\text{ then}} \cr & {\text{the antiderivatices of }}{e^{ - x}}{\text{ are:}} \cr & - \int {\left( { - {e^{ - x}}} \right)dx = } - \left( {{e^{ - x}}} \right) + C \cr & = - {e^{ - x}} + C,{\text{ where }}C{\text{ is an arbitrary constant}}{\text{.}} \cr & - {e^{ - x}} + C \cr} $$