### Home > CALC3RD > Chapter Ch5 > Lesson 5.1.4 > Problem5-46

5-46.

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

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

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

1. $f(g(x))$

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

1. $f(g(x))$

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

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

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

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