### Home > CALC > Chapter 5 > Lesson 5.1.4 > Problem5-46

5-46.

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

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

2. $f(g(x))$

3. $g(f(x))$

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

1. $\operatorname{sin}^2 x + 3\operatorname{ sin }x$

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

3. $2\operatorname{ sin }x + 3$

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

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