CPM Homework Help : CALC3RD Problem 5-53

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

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

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

Hint:

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