$$ \begin{array}{|c||c|c|c|c|} \hline x & f(x) & f'(x) & g(x) & g'(x) \\ \hline 1 & 3 & -2 & -3 & 4 \\ \hline \end{array} $$

The table above gives the values of the differentiable functions \(f\) and \(g\) and their derivatives at \(x=1\). If \(h(x)=(2f(x)+3)(1+g(x)) \), then \(h'(1)=\)

Summary Submit

$$ h(x)=(2f(x)+3)(1+g(x)) $$

Using the product rule:

$$h'(x)=(2f(x)+3)(g'(x))+(1+g(x))(2f'(x)) $$ $$ h'(1)=(2f(1)+3)(g'(1))+(1+g(1))(2f'(1)) $$ $$(2(3)+3)(4)+(1+(-3))(2(-2)) $$ $$ (9)(4)+(-2)(-4) $$ $$ 36+8 $$ $$=\boxed{44} $$