CPM Homework Help : CALC Problem 5-53

Let $f(x) = x^3$ , $g(x) = 6x-1$ , and $h(x) =\operatorname{sin }x$ . Match each function in the left column of the table with its expression in the right column.

Hint:

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

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

$3(6x − 1)^2$
$6$
$3\operatorname{ sin}^2 x$
$\operatorname{cos}(x^3)$
$3x^2$
$1$
$\operatorname{cos }x$