CPM Homework Help : CALC Problem 5-46

Let $f(x) = x^2 + 3x$ and $g(x) =\operatorname{ sin }x$ . Match the expression in the left-hand column with its simplification in the right-hand column.

$f^\prime(g(x))$
$f(g(x))$
$g(f(x))$
$g^\prime(f(x))$

$\operatorname{sin}^2 x + 3\operatorname{ sin }x$
$\operatorname{cos}(x^2 + 3x)$
$2\operatorname{ sin }x + 3$
$\operatorname{sin}(x^2 + 3x)$

Hint:

Before beginning, find $f^\prime(x)$ and $g^\prime(x)$ .