Question

Can you explain how the chain rule work in real life?

Answer 1

See below.

Explanation:

This is the best analogy I can think of.

Suppose we have `3` people.

Person a

Person b

Person c

If person b walks twice as fast as person c, we could represent this as:

`(db)/(dc)=2`

If person a walks twice as fast as person b, we could represent this as:

`(da)/(db)=2`

Now, how much faster than person c does person a walk.

Our intuition would be, if a is twice as fast as b , and b is twice as fast as c, then a is:

`2 xx 2=4` times as fast as c

This in the chain rule is:

`(da)/(dc)=(da)/(db) xx (db)/(dc)=4`

.i.e.

`(da)/(dc)=2 xx 2=4`

Hopefully from this you can see where the product of the rates of change come into play.