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

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Answer 1 · 2018-01-26T14:29:58

See below.

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.