## Calculus (3rd Edition)

The third derivative $f'''(x)$ is given by $$f'''(x)= -27 e^{12-3x}.$$
Recall that $(e^x)'=e^x$ Since we have $$f(x)= e^{12-3x}$$ then the first derivative $f'(x)$, using the chain rule, is given by $$f'(x)= e^{12-3x}(12-3x)'=-3 e^{12-3x}.$$ The second derivative $f''(x)$ is given by $$f''(x)= -3 e^{12-3x}(12-3x)'=9 e^{12-3x}.$$ The third derivative $f'''(x)$ is given by $$f'''(x)= 9e^{12-3x}(12-3x)'=-27 e^{12-3x}.$$