CPM Homework Help : APCALC Problem 11-47

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

What are $\frac { d g } { d t }$ and $\frac { d h } { d t }$ ?
Hint (a):
Use the individual functions, not the composite function.

Verify that $\frac { d g } { d h } = \frac { \frac { d g } { d t } } { \frac { d h } { d t } }$ .
Step 1(b):
$g(t)=\cos(h(t))^2$
Step 2(b):
$\frac{dg}{dh}=-\sin(h(t))^2\cdot2h(t)=?$