Calculus and Its Applications, Chapter 1, 1.6, Section 1.6, Problem 36

Differentiate $\displaystyle G(t) = (3t^5 - t^2) \left( t - \frac{5}{t} \right)$

$
\begin{equation}
\begin{aligned}
G(t) &= \left( 3t^5 \right) (t) - \left( 3t^5 \right) \left( \frac{5}{t} \right) - \left( t^2 \right) (t) + \left( t^2 \right) \left( \frac{5}{t} \right)
&& \text{Use FOIL method}\\
\\
G(t) &= 3t^6 - 15t^4 - t^3 + 5t
&& \text{Multiply variables with same bases by adding their exponents and divide variables with the same base by subtracting the exponents}
\end{aligned}
\end{equation}
$


Thus, by taking the derivative, we get

$
\begin{equation}
\begin{aligned}
G'(t) &= \frac{d}{dt} \left[ 3t^6 - 15t^4 - t^3 + 5t \right]\\
\\
&= 18t^5 - 60 t^3 - 3t^2 + 5
\end{aligned}
\end{equation}
$