Product rule applied to a polynomial product

Let $f(x) = 3x-5$ and $h(x) = x^2+2x$, so $f'(x) = 3$ and $h'(x) = 2x+2$. By the product rule, $g'(x) = f'(x)h(x) + f(x)h'(x) = 3(x^2+2x) + (3x-5)(2x+2)$.

Now evaluate at $x=1$: $h(1) = 1+2 = 3$, $f(1) = -2$, and $h'(1) = 4$. So $g'(1) = 3(3) + (-2)(4) = 9 - 8 = 1$.