Finding the derivative of a function from a table of values for other functions

Question

I have a table of values for the functions $f(x)$ and $g(x)$ and their derivatives, and I need to find the derivative of a third function based on those two functions.

Table: \begin{matrix} x & f(x) & g(x) & f'(x) & g'(x)\\ 1 & 3 & 2 & -1 & 4 \\ 2 & 5 & 3 & 7 & 1 \\ 3 & -2 & -4 & 8 & 2 \\ 4 & 0 & 6 & -3 & 9 \end{matrix}

I have the function $$h(x) = xf(x) + 4g(x)$$ and I need to find $h'(2)$.

I am assuming that I need to somehow differentiate the function, but I do not know how to find the derivative of a function that contains other functions.

Answer 1

1. Find $h'(x)$ in terms of $x, f, f', g$ and $g'$.
2. Plug in the need values at $x=2$.