Home > APCALC > Chapter 11 > Lesson 11.1.3 > Problem11-35

11-35.

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

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

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

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

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

3. Solve the identity given in part (b) for $\frac { d g } { d h }$.

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