CPM Homework Help : APCALC Problem 5-46

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

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

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

$f(g(x))$

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

$g(f(x))$

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

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

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

Hint:

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