### Home > APCALC > Chapter 5 > Lesson 5.2.1 > Problem5-53

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.

1. $f^\prime(x)$

2. $g^\prime(x)$

3. $h^\prime(x)$

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

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

6. $f ^\prime(h(x))$

7. $h ^\prime(f(x))$

1. $3(6x – 1)^2$

2. $6$

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

4. $\operatorname{cos}(x^3)$

5. $3x^2$

6. $1$

7. $\operatorname{cos}(x)$

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