Chapter 4.1, Problem 60E

To determine

To explain: why the chain rule formula $\frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx}$ is not the well-known rule for multiplying fractions.

Answer to Problem 60E

The chain rule formula $\frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx}$ is not used for multiplying fractions because $\frac{dy}{dx},\frac{dy}{du}\text{}\text{and}\frac{du}{dx}$ are not actually fractions.

Explanation of Solution

Given information:

Chain rule formula $\frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx}$ is not the well-known rule for multiplying fractions.

The chain rule formula $\frac{dy}{dx}=\frac{dy}{du}\cdot \frac{du}{dx}$ is not the rule for multiplying fractions because $\frac{dy}{dx},\frac{dy}{du}\text{}$ $\text{and}\frac{du}{dx}$ are not fractions.

They are not numerical values to be fractions.

Thus we can conclude that the chain rule is not been well-known for multiplying fractions.