Question

Differentiate  \(g(t)=4(t+1)^{2}(t-3)\) with respect to \(t\)

Answer 1

\begin{aligned}
g(t) &=4(t+1)^{2}(t-3) \\
&=4\left(t^{2}+2 t+1\right)(t-3) \\
&=4\left(t^{3}+2 t^{2}+t-3 t^{2}-6 t-3\right) \\
&=4\left(t^{3}-t^{2}-5 t-3\right) \\
&=4 t^{3}-4 t^{2}-20 t-12 \\
\therefore g^{\prime}(t) &=4\left(3 t^{2}\right)-4(2 t)-20-0 \\
&=12 t^{2}-8 t-20
\end{aligned}