The Product and Quotient Rules: z=(3t+1)(5t+2)
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pka
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\(\displaystyle \L\begin{array}{rcl}
z(t) = f(t)g(t)\quad & \Rightarrow & \quad z'(t) = f'(t)g(t) + f(t)g'(t) \\
f(t) = \left( {3t + 1} \right)\quad & \Rightarrow & \quad f'(t) = 3 \\
g(t) = \left( {5t + 2} \right)\quad & \Rightarrow & \quad g'(t) = 5 \\
\end{array}\)
z(t) = f(t)g(t)\quad & \Rightarrow & \quad z'(t) = f'(t)g(t) + f(t)g'(t) \\
f(t) = \left( {3t + 1} \right)\quad & \Rightarrow & \quad f'(t) = 3 \\
g(t) = \left( {5t + 2} \right)\quad & \Rightarrow & \quad g'(t) = 5 \\
\end{array}\)