Para calcular sua questão, vale ressaltar duas propriedades de derivação. Sendo elas:
[tex]\Large\displaystyle\text{$\begin{gathered} (x^n)'= n\cdot x^{n-1}\ \ \red{(I)}.\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} (c)'= 0\ \ \forall c\in \mathbb{R}\ \ \red{(II)}.\end{gathered}$}[/tex]
Sabendo disso, temos então que:
[tex]\Large\displaystyle\text{$\begin{gathered} -3\cdot f'(3)+4\cdot g'(4) = -3\cdot (-4)' +4\cdot (9(4)^2)\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -3\cdot f'(3)+4\cdot g'(4) = -3\cdot 0+4\cdot 144\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} -3\cdot f'(3)+4\cdot g'(4) = 0 +576\end{gathered}$}[/tex]
[tex]\Large\displaystyle\text{$\begin{gathered} \therefore \green{\underline{\boxed{-3\cdot f'(3)+4\cdot g'(4) = 576}}}\ \ (\checkmark). \end{gathered}$}[/tex]
