A more difficult
example using the Chain Rule A more difficult
example using the Chain RuleWhat would you do if you had a function within a function, within a function? Try on your own to solve the following, then follow along.
Remember the trick? What would you do first if you were to solve this equation given a value for x and only had a calculator? You would square the number and subtract 4. This is your first INNER function.
and its derivative
is:
So now your equation looks like the following.
Now, if given a value for u what would you do next? You would take it to the 4th power and add 2. The next INNER function is.
and its derivative
is:
Take a look at the equation now.
and the derivative
of this OUTER function is:
Finally, you would multiply the derivatives together.
or to facilitate
this problem in LiveMath....
equals 
or after all the substitutions:
NOTE: The use of the variables u and w in this example is arbitrary. You could use any variable. These, however, seem to be the favorites in most texts.
