If $f(x) = g(h(x))$, then:

1. Explain what each of these expressions represent: $\frac { d g } { d x } , \frac { d g } { d h } , \text { and } \frac { d h } { d x }$.

   Hint (a):

   $dg/dx$ is the rate of change of $g$ with respect to $x$.

2. Explain why $\frac { d g } { d x } = \frac { d g } { d h } \cdot \frac { d h } { d x }$.

   Hint (b):

   Since $g$ is a function of $h$ and $h$ is a function of $x$, __________________.

3. Solve $\frac { d g } { d x } = \frac { d g } { d h } \cdot \frac { d h } { d x }$ for $\frac { d g } { d h }$.

   Hint (c):

   Multiply both sides of the equation by $dx/dh$.