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

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.

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

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. $\operatorname{cos }x$