We give explanation for the product rule and chain rule.

Now that we know about differentials, let’s use them to give some intuition as to why the product and chain rules are true.

Explanation of the product rule

Linear approximations can help us explain why the product rule works.

Explanation of the chain rule

Now we’ll use linear approximations to help explain why the chain rule is true.

These ‘‘explanations’’ are not meant to be the end of the story for the product rule and chain rule, rather they are hopefully the beginning. As you learn more mathematics, these explanations will be refined and made precise.