Answer
True.
Work Step by Step
Rules of derivatives allow the derivative of a sum to be written as a sum of derivatives. Therefore, the derivative of $f$ at $x=2$ $(f'(2))$ plus the eight times the derivative of $g$ at $x=2$ $(g'(2))$ is equal to $\frac{d}{dx}[f(x)-8g(x)]$ at $x=2$.
