### Home > APCALC > Chapter 11 > Lesson 11.2.1 > Problem11-47

11-47.

Let $g(h(t)) = \cos\sqrt { t }$, $g\left(t\right)= \cos\left(t\right)$ , and $h(t) = \sqrt { t }$.

1. What are $\frac { d g } { d t }$ and $\frac { d h } { d t }$?

Use the individual functions, not the composite function.

1. Verify that $\frac { d g } { d h } = \frac { \frac { d g } { d t } } { \frac { d h } { d t } }$ .

$g(t)=\cos(h(t))^2$

$\frac{dg}{dh}=-\sin(h(t))^2\cdot2h(t)=?$