\(g(t)=4-t^2\)
\(\displaystyle g'(2)=\lim_{t\to2}\frac{g(t)-g(2)}{t-2}\)
\(\displaystyle g'(2)=\lim_{t\to2}\frac{4-t^2-0}{t-2}\)
\(\displaystyle g'(2)=-\lim_{t\to2}\frac{(2-t)(2+t)}{2-t}\)
\(\displaystyle g'(2)=-\lim_{t\to2}(2+t)\)
\(\displaystyle g'(2)=-4\)
