Chain Rule

Chain Rule Formulas

Chain Rule Basics

The chain rule is used to solve problems involving multiple quantities that are related to each other.

Direct Proportion

If two quantities $A$ and $B$ are directly proportional, then:

Indirect (Inverse) Proportion

If two quantities $A$ and $B$ are inversely proportional, then:

Combined Proportion

For combined proportion, where a quantity $Q$ depends on multiple directly or inversely proportional quantities:

where $A$ and $B$ are directly proportional to $Q$, and $C$ and $D$ are inversely proportional to $Q$.

Problem-Solving Using Chain Rule

Steps to solve problems using the chain rule:

1. Identify the quantities and their relationships (direct or inverse).
2. Set up the proportion equations based on the relationships.
3. Solve the equations to find the required quantity.

Example Problem

Suppose $A$ varies directly as $B$ and inversely as $C$. If $A_1=6$ when $B_1=4$ and $C_1=2$, find $A_2$ when $B_2=8$ and $C_2=3$.